using the hp33s for land surveying computations by jon b. purnell, pls ©2010 alidade consulting

Using the hp33sUsing the hp33s

For Land Surveying For Land Surveying ComputationsComputations

by Jon B. Purnell, PLSby Jon B. Purnell, PLS

©2010 Alidade Consulting©2010 Alidade Consulting

SynopsisSynopsis

• StrategiesStrategies• Capabilities and Capabilities and

LimitationsLimitations• Operating EssentialsOperating Essentials• Statistics FunctionsStatistics Functions• Traverse and InverseTraverse and Inverse• Memory and VariablesMemory and Variables• Equation SolverEquation Solver

Capabilities Capabilities and Limitationsand Limitations

• User programmableUser programmable– 31K of memory for 31K of memory for

programs, variables and programs, variables and user equationsuser equations

• 27 storage registers27 storage registers– For variables/dataFor variables/data

• Integrated equation Integrated equation Solver utilitySolver utility

• RPN or Algebraic entry RPN or Algebraic entry modesmodes

Capabilities Capabilities and Limitationsand Limitations

• 33rdrd Party surveying Party surveying applications are applications are available available – http://www.softwareb

ydzign.com/

• Legal for LSIT examLegal for LSIT exam– http://www.ncees.org/

exams/calculators/

http://www.softwarebydzign.com/

http://www.softwarebydzign.com/

http://www.ncees.org/exams/calculators/

http://www.ncees.org/exams/calculators/

The KeyboardThe Keyboard0.000000000.00000000

Press to power [ON] or to clear an entryPress [PURPLE] [ON] to turn unit OFF

Press to power [ON] or to clear an entryPress [PURPLE] [ON] to turn unit OFF

Press [PURPLE] + [key] to access Purple functions

Press [PURPLE] + [key] to access Purple functions

Press [TEAL] + [key] to access Teal functions

Press [TEAL] + [key] to access Teal functions

Press [key] alone to access“unshifted” functions

Press [key] alone to access“unshifted” functions

Press key when prompted for “Alpha” input

Press key when prompted for “Alpha” input

The KeyboardThe Keyboard0.000000000.00000000

Press to select operating modes: DEGrees, GRADs, RADians, and separators

Press to select operating modes: DEGrees, GRADs, RADians, and separators Press to select DISPLAY formats: FIXed, ENGineering notation, SCIentific notation, or ALL (automatic formatting)

Press to select DISPLAY formats: FIXed, ENGineering notation, SCIentific notation, or ALL (automatic formatting)

Cursor pad—click up, down, left or right to choose menu options, or scroll

Cursor pad—click up, down, left or right to choose menu options, or scroll

Setting and Setting and Changing Changing

Display FormatsDisplay Formats0.000000000.00000000

Press to open DISPLAY menu Press to open DISPLAY menu

Use Cursor Pad to select display mode, or press [1] for FIXed, [2] for SCIentific, [3] for ENGineering, or [4] for ALL

Use Cursor Pad to select display mode, or press [1] for FIXed, [2] for SCIentific, [3] for ENGineering, or [4] for ALL

EXAMPLE: to set display to show 4 FIXed decimal places:

1. Press [DISPLAY], then [1], then [4]

EXAMPLE: to set display to show 4 FIXed decimal places:

1. Press [DISPLAY], then [1], then [4]

1 F I X 2 S C I3 E N G 4 A L LFIX 4

Options appear on menu. Underlined option = current selection


0.00000.0000

Setting and Setting and Changing Changing

Angular Mode Angular Mode FormatFormat

0.00000.0000

Press to open MODES menu Press to open MODES menu

EXAMPLE: to set unit to work in DEGrees:

1. Press [MODES], then [1]

EXAMPLE: to set unit to work in DEGrees:

1. Press [MODES], then [1]

1 D E G 2 RAD3 GRAD 4 . 5,



0.00000.0000

Use Cursor Pad to select mode, or press [1] for DEGrees, [2] for RADians, [3] for GRADS, or choose [4] to use dot& comma as decimal point and 1000’s seperator

Use Cursor Pad to select mode, or press [1] for DEGrees, [2] for RADians, [3] for GRADS, or choose [4] to use dot& comma as decimal point and 1000’s seperator

The DisplayThe Display

Two lines of data

Mode icons: ALGebraic, RPN and EQuatioN entry modes,GRADs and RADians angular modes

Mode icons: ALGebraic, RPN and EQuatioN entry modes,GRADs and RADians angular modes

Current numeric system: HEXidecimal, OCTal or BINary. Blank = Decimal

HYPerbolic mode is active

Icons: [Teal] and [Purple] keys

Icons: [Teal] and [Purple] keys

Program “Flag” indicators

Program “Flag” indicators

“Alpha” keys active

“Alpha” keys active

Programming mode active

Programming mode active

ERROR!

ERROR!

Low battery

Low battery

System Busy Scrolling

mode is active

RPN: Reverse Polish Notation RPN: Reverse Polish Notation = Math without Parentheses= Math without Parentheses

• Evaluate 20 / 2+3Evaluate 20 / 2+3• RPN:RPN:

– 20 [ENTER] 2 [ENTER] 3 [+] [/] 20 [ENTER] 2 [ENTER] 3 [+] [/] (Result is 4)(Result is 4)

• Algebraic:Algebraic:– 20 [/] [(] [2] [+] [3] [)] [=] 20 [/] [(] [2] [+] [3] [)] [=]

(Result is 4)(Result is 4)

Order of operations and your Order of operations and your calculatorcalculator

Not all of these expressions yield the same answer!

Be careful how you write and enter the expression!

Not all of these expressions yield the same answer!

Be careful how you write and enter the expression!

)32(20 3220

32

20

32

20

)32(

20

=4=4=4=4

=4=4=4=4=4=4=4=4

=1=133

=1=133

=1=133

=1=133

Algebraic Mode Algebraic Mode

• Set up your calculator to operate in the ALG (Algebraic) mode

• Set up your calculator to operate in the ALG (Algebraic) mode

1. Press the 1. Press the [Purple[Purple]] keykey

1. Press the 1. Press the [Purple[Purple]] keykey

2. Press [x√y] 2. Press [x√y] 2. Press [x√y] 2. Press [x√y]

““ALG” should ALG” should appear hereappear here

““ALG” should ALG” should appear hereappear here

Back Back to our problem… to our problem… • Evaluate the expression

20 / 2+3

• Evaluate the expression20 / 2+3

1. Key in “20”1. Key in “20”1. Key in “20”1. Key in “20”

2. Press the [division] 2. Press the [division] keykey


3. Key in “2” and 3. Key in “2” and press the [addition] press the [addition] key…key……what happens?…what happens?

3. Key in “2” and 3. Key in “2” and press the [addition] press the [addition] key…key……what happens?…what happens?

4. Key in “3” and 4. Key in “3” and press [ENTER]press [ENTER]

4. Key in “3” and 4. Key in “3” and press [ENTER]press [ENTER]

Did the calculator evaluate the expression using the rules of the order of operations?


2020 20.000020 2 +10.000020 2 + 3 =13.0000

20

Let’s try it Let’s try it again… again…

• Evaluate the expression20 / (2+3)

• Evaluate the expression20 / (2+3)




3. Press the 3. Press the [Purple[Purple]] key and then press key and then press the [+/-] keythe [+/-] key

3. Press the 3. Press the [Purple[Purple]] key and then press key and then press the [+/-] keythe [+/-] key

4. Key in “2+3”4. Key in “2+3”4. Key in “2+3”4. Key in “2+3”


Are the results the same as before?

What’s different?


Are the results the same as before?

What’s different?5. Press the 5. Press the [Purple[Purple]] key and then press key and then press the [E] key, and the [E] key, and press [ENTER]press [ENTER]

5. Press the 5. Press the [Purple[Purple]] key and then press key and then press the [E] key, and the [E] key, and press [ENTER]press [ENTER]

11 keystrokes!

11 keystrokes!

20 20.000020 (20.000020 ( 2 +320 ( 2 + 3 )520 ( 2 + 3 ) =4.0000

RPN: Math without RPN: Math without parentheses parentheses

• Set up your calculator to operate in the RPN (Reverse Polish Notation) mode

• Set up your calculator to operate in the RPN (Reverse Polish Notation) mode

1. Press the 1. Press the [Teal[Teal]] keykey

1. Press the 1. Press the [Teal[Teal]] keykey

2. Press [x√y] 2. Press [x√y] 2. Press [x√y] 2. Press [x√y]

““RPN” should RPN” should appear hereappear here

““RPN” should RPN” should appear hereappear here

Using RPNUsing RPN

• Evaluate the expression20 / (2+3) using RPN

• Evaluate the expression20 / (2+3) using RPN


2. Press the [ENTER] 2. Press the [ENTER] keykey

2. Press the [ENTER] 2. Press the [ENTER] keykey

3. Key in “2” and 3. Key in “2” and press [ENTER] press [ENTER]

3. Key in “2” and 3. Key in “2” and press [ENTER] press [ENTER]

4. Key in “3” and 4. Key in “3” and press the [addition] press the [addition] keykey

4. Key in “3” and 4. Key in “3” and press the [addition] press the [addition] keykey





8 keystrokes!8 keystrokes!

0.00002020.000020.00002.00002.00002.0000320.000050.00004.0000

The StackThe Stack • Four “registers” Four “registers” (X,Y,Z and T) for (X,Y,Z and T) for temporary storage of temporary storage of values and values and intermediate resultsintermediate results

• X and Y registers X and Y registers visible on the displayvisible on the display

• Z and T registers, not Z and T registers, not visiblevisible

• Operations Operations performed on values performed on values in X and Y registersin X and Y registers

0.00000.00000.00000.0000 X register X register X register X register

T registerT registerT registerT register

Z registerZ registerZ registerZ register

Y registerY registerY registerY register

20 / (3+2) on the Stack20 / (3+2) on the Stack• Key in “20”Key in “20”• Press [ENTER]Press [ENTER]• Key in “3”, Press Key in “3”, Press

[ENTER][ENTER]• Key in “2”Key in “2”• Press [+]Press [+]• Press [Press []]

0.00000.00000.00000.0000

0.00000.00000.000020

0.00000.000020.000020.0000

0.000020.00003.00003.0000

0.000020.00003.00002

0.00000.000020.00005.0000

0.00000.00000.00004.0000 X register X register X register X register

T registerT registerT registerT register

Z registerZ registerZ registerZ register

Y registerY registerY registerY register

Stack FunctionsStack Functions

““Roll Down” (values in stack drop down 1 Roll Down” (values in stack drop down 1 register, value in X register goes to top register, value in X register goes to top (T register)(T register)

““Roll Down” (values in stack drop down 1 Roll Down” (values in stack drop down 1 register, value in X register goes to top register, value in X register goes to top (T register)(T register)

““X-Y Exchange” (values in X and Y registers X-Y Exchange” (values in X and Y registers trade places)trade places)

““X-Y Exchange” (values in X and Y registers X-Y Exchange” (values in X and Y registers trade places)trade places)

““Last X” (recalls last value stored in X Last X” (recalls last value stored in X register)register)Press Press [Teal[Teal]] [ENTER] to execute [ENTER] to execute

““Last X” (recalls last value stored in X Last X” (recalls last value stored in X register)register)Press Press [Teal[Teal]] [ENTER] to execute [ENTER] to execute

Some Functions that Some Functions that Operate on Values Operate on Values

in the X Registerin the X Register

• Key in a number, Key in a number, execute the functionexecute the function

““X Squared” [XX Squared” [X22]]““X Squared” [XX Squared” [X22]]

““Square root of X” Square root of X” [√X][√X]

““Square root of X” Square root of X” [√X][√X]

““1 over X” [1/X]1 over X” [1/X]““1 over X” [1/X]1 over X” [1/X]

““Trig Functions” [SIN] Trig Functions” [SIN] [COS] [TAN] [ASIN] [COS] [TAN] [ASIN] [ACOS] [ATAN][ACOS] [ATAN]

““Trig Functions” [SIN] Trig Functions” [SIN] [COS] [TAN] [ASIN] [COS] [TAN] [ASIN] [ACOS] [ATAN][ACOS] [ATAN]

Unit ConversionsUnit Conversions

• The hp33s ships with several built The hp33s ships with several built in unit conversionsin unit conversions– Sexagesimal Units (Decimal Degrees Sexagesimal Units (Decimal Degrees

and Degrees Minutes and Seconds)and Degrees Minutes and Seconds)– Centigrade and FarenheitCentigrade and Farenheit– Inches and CentimetersInches and Centimeters

Sexagesimal UnitsSexagesimal Units

• When finding the Sine, Cosine or When finding the Sine, Cosine or Tangent of an angle, you must:Tangent of an angle, you must:– Enter the value in degrees, minutes Enter the value in degrees, minutes

and seconds…and seconds…– ……thenthen, convert the value to decimal , convert the value to decimal

degrees…degrees…– ……thenthen get the Sine, Cosine or get the Sine, Cosine or

TangentTangent

Finding a Sine, Finding a Sine, Cosine or TangentCosine or Tangent

Result is 20.1528Result is 20.1528°°Result is 20.1528Result is 20.1528°°

Convert the D.MS value to Decimal Convert the D.MS value to Decimal degrees: Press the degrees: Press the [TEAL[TEAL]] key, key, then press [then press [HR]HR]

Convert the D.MS value to Decimal Convert the D.MS value to Decimal degrees: Press the degrees: Press the [TEAL[TEAL]] key, key, then press [then press [HR]HR]

Key in the value in D.MS format: Key in the value in D.MS format: 20.091020.0910

Key in the value in D.MS format: Key in the value in D.MS format: 20.091020.0910

Press Press [COS][COS]

Press Press [COS][COS]

Find the Cosine of 20º09’10”

Find the Cosine of 20º09’10”

0.000020.0910

Result is 0.9388 Result is 0.9388 (rounded!)(rounded!)

Result is 0.9388 Result is 0.9388 (rounded!)(rounded!)

0.000020.15280.00000.9388

Sexagesimal MathSexagesimal Math

• When adding, subtracting, When adding, subtracting, multiplying or dividing, (etc.) an multiplying or dividing, (etc.) an angle, you must:angle, you must:– Enter the values in degrees, minutes Enter the values in degrees, minutes

and seconds…and seconds…– ……thenthen, convert the values to decimal , convert the values to decimal

degrees…degrees…– ……thenthen perform the operation perform the operation– ……then convert the result to D.MS then convert the result to D.MS

formatformat

Sexagesimal Math Sexagesimal Math Example 1Example 1

Key in the value “2.30”, press the Key in the value “2.30”, press the [TEAL[TEAL]] key, then press [ key, then press [HR]HR]

Key in the value “2.30”, press the Key in the value “2.30”, press the [TEAL[TEAL]] key, then press [ key, then press [HR]HR]

Key in the value 2, press the [Key in the value 2, press the [] key] keyKey in the value 2, press the [Key in the value 2, press the [] key] key

Key in the value “5.2514”, press Key in the value “5.2514”, press [ENTER][ENTER]

Key in the value “5.2514”, press Key in the value “5.2514”, press [ENTER][ENTER]

Convert result to D.MS format:Convert result to D.MS format:Press Press [PURPLE[PURPLE]] key, then press key, then press [[HMS]HMS]

Convert result to D.MS format:Convert result to D.MS format:Press Press [PURPLE[PURPLE]] key, then press key, then press [[HMS]HMS]

Problem: Find the angle from a PC to a POC at 525.14 feet from the PC (degree of curvature = 2°30’)

Solution: Angle = 5.2514 x (2°30’) /2

Problem: Find the angle from a PC to a POC at 525.14 feet from the PC (degree of curvature = 2°30’)

Solution: Angle = 5.2514 x (2°30’) /2

5.25145.2514

Result is 6.3351 Result is 6.3351 which is which is 66°°33’51”33’51”

Result is 6.3351 Result is 6.3351 which is which is 66°°33’51”33’51”

5.25152.55.25141.2500

Press the [Press the [xx] key. Result is 6.5643] key. Result is 6.5643°°Press the [Press the [xx] key. Result is 6.5643] key. Result is 6.5643°°

0.00006.56430.00006.3351

Sexagesimal Math Sexagesimal Math Example 2Example 2

0.00000.0000

Problem: Find the Weighted Mean Azimuth of Line 1 and Line 2

Line 1 = 97°05’21” – 656.89 feetLine 2 = 92°56’05” -2607.00 feet

Solution =



Solution = 21

2211_

DistDist

DistAzmDistAzmAzimuthWeighted

Sexagesimal Math Sexagesimal Math ExampleExample

Key in the value “656.89”…then press the [Key in the value “656.89”…then press the [xx] ] keykey

Key in the value “656.89”…then press the [Key in the value “656.89”…then press the [xx] ] keykey

Key in the value “92.5605”, press the Key in the value “92.5605”, press the [TEAL[TEAL]] key, then press [key, then press [HR], then press [ENTER]HR], then press [ENTER]




0.000097.0521

Key in the value “2607.00”…then press the [Key in the value “2607.00”…then press the [xx] ] keykey….next, press the [+] key….next, press the [+] key

Key in the value “2607.00”…then press the [Key in the value “2607.00”…then press the [xx] ] keykey….next, press the [+] key….next, press the [+] key


Solution =


Solution =

21

2211_

DistDist


97.089297.089297.0892656.890.000063776.902763776.902792.934792.93472607.000063,776.9027242280.8208

The result, 306,057.7235 is the numerator in The result, 306,057.7235 is the numerator in the equation….the equation….

The result, 306,057.7235 is the numerator in The result, 306,057.7235 is the numerator in the equation….the equation….

0.0000306,057.7235

Sexagesimal Math Sexagesimal Math ExampleExample

Press the [Press the [] key…the result 93.7708] key…the result 93.7708° ° is the is the weighted mean azimuth of the line in weighted mean azimuth of the line in Decimal DegreesDecimal Degrees

Press the [Press the [] key…the result 93.7708] key…the result 93.7708° ° is the is the weighted mean azimuth of the line in weighted mean azimuth of the line in Decimal DegreesDecimal Degrees

Key in the value “2607.00”…then press the Key in the value “2607.00”…then press the

[[++] key…the result, 3263.8900 is the ] key…the result, 3263.8900 is the denominator in the equation….denominator in the equation….

Key in the value “2607.00”…then press the Key in the value “2607.00”…then press the

[[++] key…the result, 3263.8900 is the ] key…the result, 3263.8900 is the denominator in the equation….denominator in the equation….

Next, key in the value “656.89”,and press Next, key in the value “656.89”,and press [ENTER][ENTER]

Next, key in the value “656.89”,and press Next, key in the value “656.89”,and press [ENTER][ENTER]

656.8900656.8900

Convert result to D.MS format:Convert result to D.MS format:Press Press [PURPLE[PURPLE]] key, then press [ key, then press [HMS]HMS]

Convert result to D.MS format:Convert result to D.MS format:Press Press [PURPLE[PURPLE]] key, then press [ key, then press [HMS]HMS]


Solution =


Solution =

21

2211_

DistDist


656.89002607.00306,057.72353263.89000.000093.77080.000093.4615

The result is 93The result is 93°°46’15”46’15”The result is 93The result is 93°°46’15”46’15”

Statistics functionsStatistics functions

• Entering observationsEntering observations• Getting nGetting n• Getting the mean of the setGetting the mean of the set• Standard deviation of a populationStandard deviation of a population• Standard deviation of a sampleStandard deviation of a sample

Statistics FunctionsStatistics FunctionsFunctioFunctionn

DescriptionDescription KeystrokesKeystrokes

Enter observations into stats registersEnter observations into stats registers [ [

Delete observations from stats registersDelete observations from stats registers [TEAL[TEAL]] [ [

CLEARCLEAR Clear stats registersClear stats registers [TEAL[TEAL] ] [CLEAR] [4][CLEAR] [4]

SUMSSUMS View SUMMATIONS MenuView SUMMATIONS Menu [PURPLE[PURPLE] ] [SUMS][SUMS]

nn Number of observations in data setNumber of observations in data set Access via SUMS menuAccess via SUMS menu

xx

Sum of x valuesSum of x values Access via SUMS menuAccess via SUMS menu

yy

Sum of y valuesSum of y values Access via SUMS menuAccess via SUMS menu

xx22

Sum of squared x valuesSum of squared x values Access via SUMS menuAccess via SUMS menu

yy22

Sum of squared y valuesSum of squared y values Access via SUMS menuAccess via SUMS menu

Summary Statistics FunctionsSummary Statistics FunctionsFunctioFunctionn

DescriptionDescription KeystrokesKeystrokes

View MEANS MenuView MEANS Menu [PURPLE[PURPLE] ] [ ][ ]

Mean of x valuesMean of x values Access via MEANS menuAccess via MEANS menu

Mean of y valuesMean of y values Access via MEANS menuAccess via MEANS menu

Weighted mean of x valuesWeighted mean of x values Access via MEANS menuAccess via MEANS menu

SS,, View Standard Deviation MenuView Standard Deviation Menu [PURPLE[PURPLE] ] [S[S,,

SxSx Sample Standard Deviation of x valuesSample Standard Deviation of x values Access via SD menuAccess via SD menu

SSyy

Sample Standard Deviation of y valuesSample Standard Deviation of y values Access via SD menuAccess via SD menu

xx

Population Standard Deviation of x Population Standard Deviation of x valuesvalues Access via SD menuAccess via SD menu

yy

Population Standard Deviation of y Population Standard Deviation of y valuesvalues Access via SD menuAccess via SD menu

yx

x

y

yx

wx

Statistics Example 1Statistics Example 10.00000.0000





Clear STATS Registers, press: Clear STATS Registers, press: [TEAL[TEAL] ] [CLEAR] [CLEAR] [4][4]


Key in “656.89”, press Key in “656.89”, press [ENTER][ENTER]


1 X 2 VARS3 ALL 4 656.8900656.8900

Key in “97.0521”, press Key in “97.0521”, press [TEAL[TEAL] ] [[HR]HR]Key in “97.0521”, press Key in “97.0521”, press [TEAL[TEAL] ] [[HR]HR]

656.890097.0892

Press [ Press [ ]]Press [ Press [ ]]

656.89001.0000



2607.00002607.0000

Key in “92.5605”, press Key in “92.5605”, press [TEAL[TEAL]][[HR]HR]

Key in “92.5605”, press Key in “92.5605”, press [TEAL[TEAL]][[HR]HR]

2607.000092.9347

Press Press [ [ ]]

Press Press [ [ ]]

2607.00002.0000

Press Press [PURPLE[PURPLE] ] [Y[YXX], and select 3], and select 3rdrd option… option…result is weighted mean azimuth in Decimal result is weighted mean azimuth in Decimal DegreesDegrees

x y x W93.7708

Press [ENTER], press Press [ENTER], press [PURPLE[PURPLE]] [[HMS]…result HMS]…result is weighted mean azimuth in Deg.MinSec is weighted mean azimuth in Deg.MinSec formatformat

Press [ENTER], press Press [ENTER], press [PURPLE[PURPLE]] [[HMS]…result HMS]…result is weighted mean azimuth in Deg.MinSec is weighted mean azimuth in Deg.MinSec formatformat

2607.000093.4615

0.00000.0000

Statistics Example 2Statistics Example 20.000020.0000



Key in each Key in each valuevalue from the table, from the table, press [ press [ ] after each entry] after each entry

Key in each Key in each valuevalue from the table, from the table, press [ press [ ] after each entry] after each entry

Problem: Find the 95% Standard Deviation of the following set of 20 observations:

Problem: Find the 95% Standard Deviation of the following set of 20 observations:No. Value No. Value No. Value No. Value1 50 6 52 11 51 16 532 51 7 52 12 52 17 523 52 8 53 13 52 18 514 50 9 52 14 55 19 525 59 10 52 15 52 20 54

Press Press [PURPLE], [PURPLE], [S,[S,] to view ] to view Sample Standard Deviation (or Sample Standard Deviation (or Sx) at the 1 Sigma levelSx) at the 1 Sigma level

Press Press [PURPLE], [PURPLE], [S,[S,] to view ] to view Sample Standard Deviation (or Sample Standard Deviation (or Sx) at the 1 Sigma levelSx) at the 1 Sigma level

Sx Sy xy1.9541

Press [ENTER] to copy the result to Press [ENTER] to copy the result to the X register. the X register.

Key in “1.96” and press [multiply]. Key in “1.96” and press [multiply]. Result is Standard Deviation of Result is Standard Deviation of set at 95% confidence levelset at 95% confidence level

Press [ENTER] to copy the result to Press [ENTER] to copy the result to the X register. the X register.

Key in “1.96” and press [multiply]. Key in “1.96” and press [multiply]. Result is Standard Deviation of Result is Standard Deviation of set at 95% confidence levelset at 95% confidence level

0.00001.95411.95411.960.00003.8300

Vectors and vector addition Vectors and vector addition (Traverse and Inverse)(Traverse and Inverse)

• You can do these COGO You can do these COGO computations with your hp33s (as computations with your hp33s (as is, with no additional programming)is, with no additional programming)– Compute latitudes and departures, Compute latitudes and departures,

given the azimuth and length of a linegiven the azimuth and length of a line– Compute azimuth and distance, given Compute azimuth and distance, given

the coordinates of the end points of a the coordinates of the end points of a lineline

– Carry coordinates (traverse) Carry coordinates (traverse)

Traversing with your hp33s Traversing with your hp33s (STATS method)(STATS method)

• There are a couple of ways to do this…here is one There are a couple of ways to do this…here is one approach that uses the STATS registers for storing the approach that uses the STATS registers for storing the current coordinatecurrent coordinate

1.1. Clear the STATS registersClear the STATS registers2.2. Load starting Northing and Easting into STATS registersLoad starting Northing and Easting into STATS registers3.3. Key in an azimuth in D.MS formatKey in an azimuth in D.MS format4.4. Convert the azimuth to decimal degrees formatConvert the azimuth to decimal degrees format5.5. Enter a distanceEnter a distance6.6. Convert from Polar to Rectangular notationConvert from Polar to Rectangular notation7.7. Exchange contents of X<>Y registersExchange contents of X<>Y registers8.8. Add Latitude and Departure to STATS registersAdd Latitude and Departure to STATS registers9.9. Go to Step 3 and repeat process Go to Step 3 and repeat process

Step 7 ensures that the current Step 7 ensures that the current Northing will be stored in the Northing will be stored in the ““y” register, and that the y” register, and that the current Easting will be stored current Easting will be stored in the “in the “x” registerx” register

Step 7 ensures that the current Step 7 ensures that the current Northing will be stored in the Northing will be stored in the ““y” register, and that the y” register, and that the current Easting will be stored current Easting will be stored in the “in the “x” registerx” register

Traverse Example Traverse Example Using STATS registersUsing STATS registers

Step 1: Clear STATS Registers: press Step 1: Clear STATS Registers: press [TEAL[TEAL] ] [CLEAR] [4][CLEAR] [4]

Step 1: Clear STATS Registers: press Step 1: Clear STATS Registers: press [TEAL[TEAL] ] [CLEAR] [4][CLEAR] [4]

Step 2: Load Start N and E into STATS Registers: Step 2: Load Start N and E into STATS Registers: Key in 1000, press [ENTER]. (=Y coordinate = Key in 1000, press [ENTER]. (=Y coordinate = N) N) Key in 5000, press [ Key in 5000, press [ ]. (=X coordinate = E)]. (=X coordinate = E)

Step 2: Load Start N and E into STATS Registers: Step 2: Load Start N and E into STATS Registers: Key in 1000, press [ENTER]. (=Y coordinate = Key in 1000, press [ENTER]. (=Y coordinate = N) N) Key in 5000, press [ Key in 5000, press [ ]. (=X coordinate = E)]. (=X coordinate = E)

0.00000.00001 X 2 VARS3 ALL 4 0.00001000

Steps 3-4: Load the Azimuth of the line, Steps 3-4: Load the Azimuth of the line, 10º38’24”: 10º38’24”: Key in 10.3824, press Key in 10.3824, press [TEAL[TEAL] ] [[HR] HR]


Step 5: Load the Distance, 85.31: Key in 85.31 Step 5: Load the Distance, 85.31: Key in 85.31 Step 5: Load the Distance, 85.31: Key in 85.31 Step 5: Load the Distance, 85.31: Key in 85.31

Step 6: Convert from Polar to Rectangular Step 6: Convert from Polar to Rectangular notation: Press notation: Press [PURPLE[PURPLE]] [ [Y,X] Y,X]


Step 7: Exchange contents of x and y registers: Step 7: Exchange contents of x and y registers: Press [x<>y] Press [x<>y]


Step 8: Compute and store new coordinate: Step 8: Compute and store new coordinate: Press [ Press [ +] +]

To continue traversing, go to step 3 and repeat.To continue traversing, go to step 3 and repeat.

1000.00001000.00001000.000050001000.00001.00001000.000010.38241000.000010.640010.640085.3115.751483.843283.843215.751483.84322.0000

Traversing with your hp33s Traversing with your hp33s (STATS method)(STATS method)

DISADVANTAGES:Current coordinate does not appear on “stack”Must use [SUMS] function to view x (easting) and y (northing)

DISADVANTAGES:Current coordinate does not appear on “stack”Must use [SUMS] function to view x (easting) and y (northing)

Traversing with your hp33s Traversing with your hp33s (Complex Operations (Complex Operations

Method)Method)• Complex Operations can be used to do arithmetic on Complex Operations can be used to do arithmetic on

pairs of numbers. We’ll use this capability to compute pairs of numbers. We’ll use this capability to compute coordinate pairs (Northings and Eastings)coordinate pairs (Northings and Eastings)

1.1. Load starting Northing and Easting into “y” and “x” Load starting Northing and Easting into “y” and “x” registers registers

2.2. Key in an azimuth in D.MS formatKey in an azimuth in D.MS format3.3. Convert the azimuth to decimal degrees formatConvert the azimuth to decimal degrees format4.4. Enter a distanceEnter a distance5.5. Convert from Polar to Rectangular notationConvert from Polar to Rectangular notation6.6. Exchange contents of X<>Y registersExchange contents of X<>Y registers7.7. Add Latitude and Departure to “y” and “x” registers Add Latitude and Departure to “y” and “x” registers

using “complex addition” functionusing “complex addition” function8.8. Go to Step 2 and repeat process Go to Step 2 and repeat process Step 6 ensures that the current Step 6 ensures that the current

Northing will be stored in the Northing will be stored in the “y” register, and that the “y” register, and that the current Easting will be stored current Easting will be stored in the “x” registerin the “x” register

Step 6 ensures that the current Step 6 ensures that the current Northing will be stored in the Northing will be stored in the “y” register, and that the “y” register, and that the current Easting will be stored current Easting will be stored in the “x” registerin the “x” register

Traverse Example Traverse Example Using Complex mathUsing Complex math

Step 1: Load Staring N and E into y and x Step 1: Load Staring N and E into y and x Registers: Registers: Key in 1000, press [ENTER]. (=Y coordinate = Key in 1000, press [ENTER]. (=Y coordinate = N) N) Key in 5000, press [ENTER]. (=X coordinate = Key in 5000, press [ENTER]. (=X coordinate = E)E)

Step 1: Load Staring N and E into y and x Step 1: Load Staring N and E into y and x Registers: Registers: Key in 1000, press [ENTER]. (=Y coordinate = Key in 1000, press [ENTER]. (=Y coordinate = N) N) Key in 5000, press [ENTER]. (=X coordinate = Key in 5000, press [ENTER]. (=X coordinate = E)E)



Step 4: Load the Distance, 85.31: Key in 85.31 Step 4: Load the Distance, 85.31: Key in 85.31 Step 4: Load the Distance, 85.31: Key in 85.31 Step 4: Load the Distance, 85.31: Key in 85.31





Step 7: Compute new coordinate: Step 7: Compute new coordinate: Press Press [TEAL[TEAL]] [COMPLEX] [+] [COMPLEX] [+]

To continue traversing, go to step 3 and repeat.To continue traversing, go to step 3 and repeat.

0.00000.00000.000010001000.00001000.00001000.000050005000.00005000.00005000.000010.38245000.000010.640010.640085.3115.751483.843283.843215.75141083.84325015.7514

Traversing with your hp33s Traversing with your hp33s (Complex Operations (Complex Operations

Method)Method)ADVANTAGES:

Coordinates appear on the stack. Northing is in the “y” register, Easting is in the “x” register

DISADVANTAGES:Coordinates are not storedNo way to “back up” one course

ADVANTAGES: Coordinates appear on the stack. Northing is in the “y” register, Easting is in the “x” register

DISADVANTAGES:Coordinates are not storedNo way to “back up” one course

Inversing with your hp33s Inversing with your hp33s (Complex Operations (Complex Operations

Method)Method)The Complex Math functions make computing a distance The Complex Math functions make computing a distance

and direction between two points pretty simple. and direction between two points pretty simple. Here’s how:Here’s how:

1.1. Load Northing and Easting of TO point in stackLoad Northing and Easting of TO point in stack2.2. Load Northing and Easting of FROM point in stackLoad Northing and Easting of FROM point in stack3.3. Use Complex Math to find Latitude and DepartureUse Complex Math to find Latitude and Departure4.4. Exchange contents of X<>Y registers Exchange contents of X<>Y registers 5.5. Convert from Rectangular to Polar notation formatConvert from Rectangular to Polar notation format6.6. Value in “y” is Value in “y” is ΘΘ or direction of line, with respect to north. or direction of line, with respect to north.

If If ΘΘ is positive, it = the Azimuth of the line in HR format. is positive, it = the Azimuth of the line in HR format.If If ΘΘ is negative, add 360 is negative, add 360°° to to ΘΘ to get Azimuth of the line to get Azimuth of the line in HR format.in HR format.

7.7. Convert Azimuth of the line to HMS format. Convert Azimuth of the line to HMS format. Step 4 ensures that Step 4 ensures that ΘΘ will be will be reckoned with respect to reckoned with respect to NorthNorth

Inversing Example Inversing Example

Steps 1-2: Load Coordinates in stack: Steps 1-2: Load Coordinates in stack: Key in Northing of TO point, press [ENTER]Key in Northing of TO point, press [ENTER]Key in Easting of TO point, press [ENTER]Key in Easting of TO point, press [ENTER]Key in Northing of FROM point, press [ENTER]Key in Northing of FROM point, press [ENTER]Key in Easting of FROM point. Stop here!Key in Easting of FROM point. Stop here!

Steps 1-2: Load Coordinates in stack: Steps 1-2: Load Coordinates in stack: Key in Northing of TO point, press [ENTER]Key in Northing of TO point, press [ENTER]Key in Easting of TO point, press [ENTER]Key in Easting of TO point, press [ENTER]Key in Northing of FROM point, press [ENTER]Key in Northing of FROM point, press [ENTER]Key in Easting of FROM point. Stop here!Key in Easting of FROM point. Stop here!

Step3: Find Latitude and Departure: Step3: Find Latitude and Departure: Press Press [TEAL[TEAL] ] [CMPLX] [-] [CMPLX] [-]

Step3: Find Latitude and Departure: Step3: Find Latitude and Departure: Press Press [TEAL[TEAL] ] [CMPLX] [-] [CMPLX] [-]



Step 5: Convert from Rectangular to Polar Step 5: Convert from Rectangular to Polar notation: Press notation: Press [TEAL[TEAL]] [[ΘΘ,r,r] ]

Step 5: Convert from Rectangular to Polar Step 5: Convert from Rectangular to Polar notation: Press notation: Press [TEAL[TEAL]] [[ΘΘ,r,r] ]

Value in “y” is Θ, or direction of line, Value in “y” is Θ, or direction of line, with with respect to northrespect to north, in decimal degrees format, in decimal degrees format

Value in “x” is distance Value in “x” is distance

Value in “y” is Θ, or direction of line, Value in “y” is Θ, or direction of line, with with respect to northrespect to north, in decimal degrees format, in decimal degrees format

Value in “x” is distance Value in “x” is distance

0.00000.0000392,128.98901,107,817.5790390,522.56901,118,227.356_1,606.4200-10,409.7770-10,409.77701,606.4200-81.227410,532.997810,532.9978-81.2274-81.227436010,532.9978278.772610,532.9978278.4621

Problem: Find azimuth and distance from Knapp to Sand

Problem: Find azimuth and distance from Knapp to Sand

STATION NORTHING (Y) EASTING (X)

To "Sand" 392,128.989 1,107,817.579

From "Knapp" 390,522.569 1,118,227.356

MemoryMemory

• Hp33s has 31K of memoryHp33s has 31K of memory• You can storeYou can store

– NumbersNumbers– EquationsEquations– ProgramsPrograms

• 27+ user accessible memory registers27+ user accessible memory registers– Registers A though Z, i, (plus STATS registers) Registers A though Z, i, (plus STATS registers)

Storing an Storing an often used numberoften used number

Meters to US Survey Feet: 1 meter ≈ 3.2808333333 US Survey feet

You can store this number in a storage register for later use

Meters to US Survey Feet: 1 meter ≈ 3.2808333333 US Survey feet

You can store this number in a storage register for later use

Key in value you want to store…Key in value you want to store…3.28083333333, then press [STO]3.28083333333, then press [STO]

Key in value you want to store…Key in value you want to store…3.28083333333, then press [STO]3.28083333333, then press [STO]

STO _

Next, choose a register in which to store the Next, choose a register in which to store the number (select a letter, from A to Z… We number (select a letter, from A to Z… We will store this value in register U):will store this value in register U):

Press [U] to store the value in register UPress [U] to store the value in register U

Next, choose a register in which to store the Next, choose a register in which to store the number (select a letter, from A to Z… We number (select a letter, from A to Z… We will store this value in register U):will store this value in register U):

Press [U] to store the value in register UPress [U] to store the value in register U

Math with Math with Stored numbersStored numbers

Using the stored Meters-to-US foot conversion, convert these metric coordinates to State Plane values:

119,521.155mN, 337,663.473mE

Using the stored Meters-to-US foot conversion, convert these metric coordinates to State Plane values:

119,521.155mN, 337,663.473mE

Key in 119521.155Key in 119521.155Key in 119521.155Key in 119521.155

0.00000.0000

Press [RCL], then Press [RCL], then [U][U]


Press [Multiply]Press [Multiply]Press [Multiply]Press [Multiply]

Key in 337663.473Key in 337663.473Key in 337663.473Key in 337663.473



Press [Multiply]Press [Multiply]Press [Multiply]Press [Multiply]

0.0000 119,521.155_RCL _119,521.15503.28080.0000392,128.9894392,128.9894337,663.473_RCL _337,663.47303.2808392,128.98941,107,817.5777

Using Equations Using Equations for Problem Solvingfor Problem Solving

• Equations are sets of instructions Equations are sets of instructions that the hp33 can use to perform that the hp33 can use to perform computationscomputations

• Equations can use values stored in Equations can use values stored in variables A though Z for their variables A though Z for their computations, or they can prompt computations, or they can prompt you to supply values for the you to supply values for the variablesvariables


• Equations can be used to solve Equations can be used to solve repetitive problemsrepetitive problems

• Equations can be used to solve for Equations can be used to solve for anyany unknown in the equation unknown in the equation

• Equations can be stored for future Equations can be stored for future use, or input on-the flyuse, or input on-the fly

• Not all functions are available, see Not all functions are available, see pg. 6-15pg. 6-15


• ArcLength = 2ArcLength = 2ππR(R(ΔΔ / / 360)360)– Variable assignments:Variable assignments:– L = ArcLengthL = ArcLength– R = RadiusR = Radius– I = Central AngleI = Central Angle

• L = 2 x L = 2 x ππ x R x I/360 x R x I/360

Storing an EquationStoring an EquationStore an equation for solving the Arc Length of a horizontal curve:

L = 2 x π x R x I/360

Store an equation for solving the Arc Length of a horizontal curve:

L = 2 x π x R x I/360

Press Press [Purple[Purple]] [EQN] [EQN]Press Press [Purple[Purple]] [EQN] [EQN]

0.00000.0000

Press [RCL] then [L]Press [RCL] then [L]Press [RCL] then [L]Press [RCL] then [L]

Press [RCL] [R] [Multiply]Press [RCL] [R] [Multiply]Press [RCL] [R] [Multiply]Press [RCL] [R] [Multiply]

EQN LIST TOPEQN LIST TOPL ▐

Press Press [Purple[Purple]] [=] [=]Press Press [Purple[Purple]] [=] [=]

Press Press [Purple[Purple]] [ [ππ] ] [multiply][multiply]

Press Press [Purple[Purple]] [ [ππ] ] [multiply][multiply]

Press [RCL] [I] [Divide]Press [RCL] [I] [Divide]Press [RCL] [I] [Divide]Press [RCL] [I] [Divide]

Ken in 360, Press Ken in 360, Press [ENTER] [ENTER]

Ken in 360, Press Ken in 360, Press [ENTER] [ENTER]

Press [2] [multiply]Press [2] [multiply]Press [2] [multiply]Press [2] [multiply]

EQN LIST TOPL=▐EQN LIST TOPL=2 x▐EQN LIST TOPL= 2 x π x▐EQN LIST TOPL= 2 x π x R x▐EQN LIST TOPL= 2 x π x R x I ÷▐EQN LIST TOPL= 2 x π x R x I ÷360

Using a Using a Stored EquationStored Equation

Use Stored Arc Length equation for finding the Length of a horizontal curve with these parameters:Radius = 114.59 feetCentral angle = 71°21’17”

Use Stored Arc Length equation for finding the Length of a horizontal curve with these parameters:Radius = 114.59 feetCentral angle = 71°21’17”


0.00000.0000

Scroll up or down if necessary to select Scroll up or down if necessary to select desired equation, and press [ENTER]desired equation, and press [ENTER]

Scroll up or down if necessary to select Scroll up or down if necessary to select desired equation, and press [ENTER]desired equation, and press [ENTER]

EQN LIST TOPL= 2 x π x R x I ÷360R?114.59

At the prompt “R?” key in the curve’s At the prompt “R?” key in the curve’s radius, or 114.59, and press [R/S]radius, or 114.59, and press [R/S]

At the prompt “R?” key in the curve’s At the prompt “R?” key in the curve’s radius, or 114.59, and press [R/S]radius, or 114.59, and press [R/S]

Convert the central angle to decimal degrees: Convert the central angle to decimal degrees: Press Press [Teal[Teal]] [ [HR], then press [R/S]HR], then press [R/S]


At the prompt, “I?” key in the curve’s central At the prompt, “I?” key in the curve’s central angle in D.MS format, or 71.2117angle in D.MS format, or 71.2117

At the prompt, “I?” key in the curve’s central At the prompt, “I?” key in the curve’s central angle in D.MS format, or 71.2117angle in D.MS format, or 71.2117

I?71.2117I?71.3547L=142.7075

Result, L is displayedResult, L is displayedResult, L is displayedResult, L is displayed

Solving for Solving for an Unknown Variablean Unknown Variable

Use the Arc Length equation to solve for curve radius, given: Arc Length = 326.30 Central angle = 22°50’28”

Use the Arc Length equation to solve for curve radius, given: Arc Length = 326.30 Central angle = 22°50’28”


0.00000.0000

Scroll up or down if necessary to select Scroll up or down if necessary to select desired equation (do not press ENTER!)desired equation (do not press ENTER!)

Scroll up or down if necessary to select Scroll up or down if necessary to select desired equation (do not press ENTER!)desired equation (do not press ENTER!)

EQN LIST TOPL= 2 x π x R x I ÷360SOLVE _

Press [SOLVE], and then press the key Press [SOLVE], and then press the key associated with the variable you need to associated with the variable you need to solve for, [R] in this case.solve for, [R] in this case.

Press [SOLVE], and then press the key Press [SOLVE], and then press the key associated with the variable you need to associated with the variable you need to solve for, [R] in this case.solve for, [R] in this case.

At the prompt, “I?” key in the curve’s central At the prompt, “I?” key in the curve’s central angle in D.MS format: 22.5028angle in D.MS format: 22.5028

At the prompt, “I?” key in the curve’s central At the prompt, “I?” key in the curve’s central angle in D.MS format: 22.5028angle in D.MS format: 22.5028

At the prompt, “L?” key in the curve arc At the prompt, “L?” key in the curve arc length, 326.30, then press [R/S]length, 326.30, then press [R/S]

At the prompt, “L?” key in the curve arc At the prompt, “L?” key in the curve arc length, 326.30, then press [R/S]length, 326.30, then press [R/S]

L?326.30I?22.5028I?22.8411



R=818.5072

Selected Equation Mode OperationsSelected Equation Mode OperationsFunctionFunction DescriptionDescription KeystrokesKeystrokes

EQNEQN Enter and leave Equation modeEnter and leave Equation mode [Purple[Purple]] [EQN] [EQN]

ENTERENTER Evaluates displayed equation, stores Evaluates displayed equation, stores result in variable on left of equals signresult in variable on left of equals sign [ENTER[ENTER

RUN/STOPRUN/STOP Prompts for next variable in the Prompts for next variable in the equationequation [R/S][R/S]

CLEARCLEAR Deletes displayed equation from Deletes displayed equation from memorymemory [Teal[Teal] ] [CLEAR][CLEAR]

SOLVESOLVE Solves for a user-specified variable in an Solves for a user-specified variable in an equationequation [SOLVE][SOLVE]

DELETEDELETE Deletes rightmost character in an Deletes rightmost character in an equationequation [[]]

SCROLL SCROLL UP / DOWNUP / DOWN

Scrolls up/down through list of stored Scrolls up/down through list of stored equationsequations Cursor pad Cursor pad

SCROLL SCROLL

TOP / BOTTOMTOP / BOTTOM Jumps to top/bottom of equation listJumps to top/bottom of equation list [Teal[Teal]] + Cursor pad + Cursor pad

SHOWSHOW Used for long equations that don’t fit on Used for long equations that don’t fit on the screenthe screen [Purple[Purple]] [SHOW] [SHOW]

ExitExit Leaves Equation modeLeaves Equation mode [C][C]

Horizontal Curve Horizontal Curve EquationsEquations

100 Foot Arc Definition100 Foot Arc DefinitionHorizontal Curve EquationsHorizontal Curve Equations

NameName EquationEquation Variables Variables

Arc LengthArc Length L = 2 x L = 2 x ππ x R x I ÷ 360 x R x I ÷ 360 L = Arc Length, R = Raduis, L = Arc Length, R = Raduis, I = Central Angle in Decimal degreesI = Central Angle in Decimal degrees

Semi-Semi-TangentTangent T = R x tan( I ÷ 2 )T = R x tan( I ÷ 2 ) T = Semi-tangent, R = Radius T = Semi-tangent, R = Radius

I = Central Angle in Decimal degreesI = Central Angle in Decimal degrees

Long ChordLong Chord C = 2 x R x sin( I ÷ 2 )C = 2 x R x sin( I ÷ 2 ) C = Long Chord, R = Radius C = Long Chord, R = Radius I = Central Angle in Decimal degreesI = Central Angle in Decimal degrees

External External E = ( R ÷ cos(I ÷ 2 )) - E = ( R ÷ cos(I ÷ 2 )) - R R

E = External distance, R = Radius E = External distance, R = Radius I = Central Angle in Decimal degreesI = Central Angle in Decimal degrees

Middle Middle OrdinateOrdinate

M = R – ( R x cos(I ÷ M = R – ( R x cos(I ÷ 2 ))2 ))

M = Middle Ordinate, R = Radius M = Middle Ordinate, R = Radius I = Central Angle in Decimal degreesI = Central Angle in Decimal degrees

Degree of Degree of CruvatureCruvature D = 5729.578 ÷ RD = 5729.578 ÷ R D = Degree of Curvature in Decimal D = Degree of Curvature in Decimal

degrees, R = Radiusdegrees, R = Radius

Test DataTest Data R = 818.51, I = R = 818.51, I = 2222°°50’28”50’28”

L = 326.30, T = 165.35, C = 324.14, L = 326.30, T = 165.35, C = 324.14, E = 16.53, M = 16.21, D = 7E = 16.53, M = 16.21, D = 7°°

Horizontal Curve Horizontal Curve EquationsEquations

TrianglesTrianglesNameName EquationEquation Variables Variables Area of Right Area of Right triangletriangle Q=1/2*B*HQ=1/2*B*H Q = Area, B = Base, Q = Area, B = Base,

H = HeightH = Height

Area of Area of Oblique Oblique triangletriangle

Q=.5*A*B*sin(C)Q=.5*A*B*sin(C) Q = Area, A = Side a, B = side b, Q = Area, A = Side a, B = side b, C = Angle C in Decimal degreesC = Angle C in Decimal degrees

CoslawCoslawT=acos((B^2+C^2-T=acos((B^2+C^2-A^2)A^2)

/(2*B*C))/(2*B*C))

T = Angle A in Decimal degrees, B = T = Angle A in Decimal degrees, B = side b, C = side c, A = side aside b, C = side c, A = side a

Hero’s Hero’s FormulaFormula

Q=SQRT(.5*(A+B+C)*(.5*Q=SQRT(.5*(A+B+C)*(.5*(A+B+C)-A)*(.5*(A+B+C)-(A+B+C)-A)*(.5*(A+B+C)-B)*(.5*(A+B+C)-C))B)*(.5*(A+B+C)-C))

Q = Area, A = side a, B = side b, Q = Area, A = side a, B = side b, C = side cC = side c

Pythagorean Pythagorean TheoremTheorem C = SQRT(A^2+B^2)C = SQRT(A^2+B^2)

A = side A, B = side B, C = side CA = side A, B = side B, C = side C

Trapezoid Trapezoid AreaArea Q=(A+B)*H/2Q=(A+B)*H/2 Q = Area, A = Base 1, B = Base 2, H Q = Area, A = Base 1, B = Base 2, H

+ Height+ Height

Test DataTest Data

Right triangle: a = 60, b = Right triangle: a = 60, b = 80, 80, c = 100, A = 36c = 100, A = 36°°52’12”, 52’12”, B = 53B = 53°°07’48” C = 9007’48” C = 90°° Area = 2400Area = 2400

Trapezoid: Base 1 = 100, Base 2 = 80, Trapezoid: Base 1 = 100, Base 2 = 80,

Height = 95, Area = 8550Height = 95, Area = 8550

Sliding Area Equation for TI-89 Numeric Solver 11/09/2006 – Jon B. Purnell, PLS

Works for all trapezoids. Use to find the distance a parallel line must fall (height of a sub-trapezoid) from base1 to get a given area, or to find the area of a sub-trapezoid having a given height. Input Data:

sub-trapezoid area = 3,000,000.00 base1 = 4076.7189 base2 = 1763.1192 ht = 1713.2353 Output: solve for height of sub-trapezoid, h = 857.7407 (NOTE: the computed value “h” is measured from base 1 )

Derived from standard “area-of-a-trapezoid formula”: area = (base1+base2)*height/2 The sliding area equation substitutes “base1+(base2-base1)/ht*h” for “base 2” in the standard trapezoid area equation (see standard equation, above). In a trapezoid, the lengths of the bases are dependent upon their separation (height of the trapezoid) and upon and the difference in their lengths. It is a linear relationship: (base2-base1)/height describes it; and it can be thought of as the change in base length per unit of trapezoid height. The relationship can be used to compute the length of an unknown base of a sub-trapezoid, whose area is given as a fixed value. Then it is possible to compute the height of a sub-trapezoid whose area has been defined, as in the sample above. These kind of problems are often referred to as “sliding side area problems” or “pre-determined area problems”

Area of sub-trapezoid to be segregated from a larger whole – this equation will compute the height of the height of the sub-trapezoid given the pre-determined area of the sub-trapezoid and the height and two bases of the larger parent trapezoid.

Enter this in “eqn:” field of TI-89 Numeric Solver

• Sample Sample equation equation documentationdocumentation– Sample Sample

problemproblem– SketchSketch– Variable Variable

definitionsdefinitions– Equation Equation

formated for formated for inputinput

– ExplanationExplanation– Sample dataSample data– SolutionSolution

Thanks for your kind Thanks for your kind attention!attention!

• Contact: Jon B. Purnell, PLSContact: Jon B. Purnell, PLS– [email protected]– 360-460-8565360-460-8565

• Download this Download this Presentation atPresentation at– www.lsaw-noly.orgwww.lsaw-noly.org

mailto:[email protected]

using the hp33s for land surveying computations by jon b. purnell, pls ©2010 alidade consulting

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