exercises on right triangle formulas

7/28/2019 Exercises on Right Triangle Formulas

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Creator of all things,

true source of light and wisdom,

origin of all being,

graciously let a ray of your light penetratethe darkness of my understanding.

Take from me the double darkness

in which I have been born,

an obscurity of sin and ignorance.

Give me a keen understanding,

a retentive memory, and

the ability to grasp things

correctly and fundamentally.

Grant me the talent

of being exact in my explanations

and the ability to express myselfwith thoroughness and charm.

Point out the beginning,

direct the progress,

and help in the completion.

I ask this through Christ our Lord. Amen.

A Students PrayerSt. Thomas Aquinas


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Solutions of Right Triangles

Formulas available for Use:1. Theorem of Pythagoras

2. Six Trigonometric Ratios or Functions

Watch out pointers or reminders1. There must be, at least, 3 known quantities;

2. One of the known quantities must be a measure of length;

3. Check for consistency of units;

4. When checking your answers, use the property A + B = 90;

5. Do not use 90 - A = B or 90 - B = A for checking purposes; and6. Remember to use our agreed degrees of accuracy


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For each set of data, solve for the unknown quantities of the right triangle

shown below.

A

B

C

1. a = 25.40 cm and c = 50.80 cm

2. b = 98.23 cm and a = 125.00 cm

3. c = 125.20 cm and b = 98.65 cm

4. B = 25.0000 and b = 38.30 cm

5. A = 35.0000 and a = 48.56 cm6. A = 45.0000 and b = 16.65 cm

7. A = 55.0000 and c = 215.00 cm

8. B = 65.0000 and a = 521.00 cm

9. B = 75.0000 and b = 251.00 cm

10. B = 85.0000 and c = 512.00 cm


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a b c A B C A + B ROE

25.40 43.99 50.80 30.0000 59.9908 90.0000 89.9908 -0.01%

125.00 98.23 158.98 51.8376 38.1612 90.0000 89.9988 0.00%

77.09 98.65 125.20 38.0053 51.9934 90.0000 89.9987 0.00%82.14 38.30 90.63 65.0020 25.0000 90.0000 90.0020 0.00%

48.56 69.35 84.66 35.0000 55.0007 90.0000 90.0007 0.00%

16.65 16.65 23.55 45.0000 44.9919 90.0000 89.9919 -0.01%

176.12 123.32 215.00 55.0000 35.0003 90.0000 90.0003 0.00%

521.00 1,117.29 1,232.79 25.0000 65.0000 90.0000 90.0000 0.00%

67.24 251.00 259.85 14.9968 75.0000 90.0000 89.9968 0.00%

44.62 510.05 512.00 4.9996 85.0000 90.0000 89.9996 0.00%

Answers to the exercise problems


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Applications

Angle of Elevation, Angle of Depression, Bearings

Angle of elevation and the angle of depression are

vertical angle applications using right triangle solutions.

On the horizontal plane, bearing problems are typical

applications.


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Angle of Elevation

The vertical angle subtended by a vertical object from an exterior vertex or

viewpoint wherein the line of sight is above the horizon.

Horizon

Line of sight

Angle of Elevation

ObjectVertex or viewpoint


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Example: A man was standing at a street corner

120.00 meters from the face of a building. He

observed that the top of the building makes an

angle of 35 with the horizon. How high was thebuilding assuming that the base of the building

and the viewpoint are level to each other?


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Angle of Depression

The vertical angle subtended by a vertical object from an exterior vertex or

viewpoint wherein the line of sight is below the horizon.

Horizon

Line of sight

Angle of Depression

Object

Vertex or viewpoint


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Example: A man was standing at topmost ledge of a hotel building that was

40.00 meters high. He observed that a fountain in the plaza made an angle of

depression of 65. How far was the fountain from the ledge?

A

A


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Bearings

The direction of any horizontal line with respect to the y-axis maybe defined by means of bearings, azimuths, deflection angles,

angles to the right, or interior angles.

The bearing of a line is indicated by the quadrant in which the line

falls and the acute angle which the line makes with either the

positive or negative y-axis.

Bearings are said to be observed bearings when taken from the

field or calculated bearings when obtained by computation.

(Surveying: Davis, Foote and Kelly)


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EW

S

N

Bearingangle

The bearing of a line is indicated by the quadrant in which the line falls and the

acute angle which the line makes with either the positive or negative y-axis.


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Examples:

1. N 3527 E

2. N 4235 W3. S 1828 W

4. S 7212 E

EW

S

N

PROBLEM: A ship travels N2820E for 86 km after which it changes direction

to N6140W for 124 km. How far is the ship from its starting point?


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Exercises: Angle of Elevation and Angle of Depression

1. Cadet Santiago was standing 150 meters from the base of a flagpole. What

is the height of the flagpole if the angle of elevation is 40?

2. The distance between the bases of two skyscrapers was measured to be

37.5 meters. What is the height of one skyscraper if the angle of elevation

is 6530?3. Shaquille ONeal was meditating one sunny day. He was standing on a

basketball court and he found that at about 9:30 the shadow that he cast

on the hard court was 1.82 meters long. If his height is 2.24 meters, what

was the angle of depression of his shadow at that time?

4. Godofredo and his survey party reached the apex of Hill 42 and observed

that the angle of depression of a sea craft on the shore made was

371630. If Hill 42, according to the topographic map is 120 meters above

mean sea level, what was the horizontal distance between the sea craft

and the apex of the hill?


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Exercises: Bearings1. An observer in a ship sailing on a course of N5030E observed a

lighthouse with bearing N2030E. After traveling 15 km on its

course, the observer took another reading and found that the

lighthouse now has a bearing of N3930W. How far was the ship

at each time of the two readings?

2. From an airport, an airplane and a helicopter travel to two

different islands. The plane travels 235 km at a bearing of

N6550E. The helicopter travels S2410E for 138 km. How far

apart are the two islands?

3. A yacht travels N1330W from the marina for 126 km. At thatpoint, It travels S7630W for 178 km. What is its latest position,

i.e. distance and bearing, from the marina?

exercises on right triangle formulas

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