fieldwork 8 (2nd draft)

7/24/2019 Fieldwork 8 (2nd Draft)

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II. INTRODUCTION

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in

geometry. A triangle with vertices A, B, and C is denoted triangle ABC. The base of a triangle can

be any one of the three sides, usually the one drawn at the bottom. You can pick any side you like

to be the base. Commonly used as a reference side for calculating the area of the triangle. In an

isosceles triangle, the base is usually taken to be the unequal side. The altitude of a triangle is the

perpendicular from the base to the opposite vertex. (The base may need to be extended). Since

there are three possible bases, there are also three possible altitudes. The three altitudes intersect

at a single point, called the orthocenter of the triangle. In the field we are going to determine the

height of a remote point using these principles.


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III. OBJECTIVES AND INSTRUMENTS

OBJECTIVES

1. To develop the skills in the vertical distance of a certain inaccessible point using a

single vertical plane using two planes, horizontal and vertical.2. To apply the knowledge learned in the analysis of right triangles in determining the

height of a remote point.

3. To learn how to read vertical angle in the transit.

4. To have the confidence of working with ones party of group and to be fully

responsible in the performance of the assigned task.

INSTRUMENTS

1. Theodolite 2. Chalk

- An instrument similar to an ordinary - A soft compact calcite with

surveyor's level but capable of finer varying amounts of silica, quartz,

readings and including a prism arrangement feldspar, or other mineral impurities,

that permits simultaneous observation generally gray-white or yellow-white

of the rod and the leveling bubble. and derived chiefly from fossil

3. Leveling Rod 4. Plumb bobs

- used with a levelling instrument to - is a weight, usually with a pointed tip

determine the difference in height on the bottom, which is suspended

between points or heights of points above from a string and used as a vertical

a datum surface. reference line


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IV. PROCEDURE & COMPUTATIONS

A.

Determination of the height of a flagpole as the remote point using a single vertical

plane

1.

Set up the transit at a convenient location and call it point A where one can see clearly the

leveling rod the topmost part of the flagpole.

2. Using the normal form of the telescope, sight the topmost part of the flagpole. Record the

reading on the vertical circle, call it angle a.

3. For the second trial, use inverted telescope to view the remote point. This is done to

determine the index error of the instrument.

4. Get the mean of the two readings and record it as the mean of angle a or the angle of

elevation of the remote point from the first station.

5. Set the leveling rod vertically near the flagpole and level the telescope of the transit. Sight

the reading to get the height of the instrument on its initial location.

6. Move the transit towards the flagpole and call it station B, the measure its distance from its

initial location. Record this as distance AB.

7. After leveling the transit, sight the top of the flagpole twice, again using the normal and

inverted position of the telescope for the two trials. Record the two vertical angle readings.

Determine the mean of the two readings and call it mean angle b.

8. Level the telescope, and get the height of the instrument by sighting the leveling rod at the

base of the flagpole. This will represent the height of the instrument on station b.

9. Analyze the two right triangles formed to determine the height of the remote point.


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COMPUTATION:

The computation of sample field notes is done in accordance with the steps listed here under:

Computation of an the height of the remote point

Determine the difference in elevation between the two instruments set-ups.

. =

Analyze triangle BEF, solve for the distance x for the analysis of the oblique triangle.

=

Determine the sum of the distance AB and x for the analysis of the oblique triangle.

= +

Using sine law in the oblique triangle AFD, solve for the distance FD.

+ ( )

=

Using the right triangle, FDG, solve for the height of the remote point DG.

=


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VIII. RESEARCH AND DISCUSSION

This fieldwork is all about the determination of the height of the remote point which

involves using the angle of depression or elevation to an object and knowing how far away the

object is and it enable us to find the height of the object using trigonometry. The disadvantage ofdoing this is that it is very difficult to measure the height of a mountain or the depth of a canyon

directly and it is much easier to measure how far away it is and to measure the angle of depression

and elevation.

In this fieldwork, we have measured the height of the remote point by setting up first the

theodolite. Then, we sighted the topmost part of the flagpole and determine its angle from the

ground. After that, we measured for the height of the theodolite in its initial location for us to

compute for the height of the building to its flagpole. This is the illustration about the trigonometric

method that we did for this fieldwork.

In planar geometry, an angle is the figure formed by two rays, called the sides of the angle,

sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a

plane, but this plane does not have to be a Euclidean plane.

The tangent of an angle is the ratio of the length of the opposite side to the length of the

adjacent side: so called because it can be represented as a line segment tangent to the circle, that

is the line that touches the circle, from Latin linea tangens or touching line (cf. tangere, to touch)


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IX. CONCLUSION

In this fieldwork, the thing that we must learn is on how to use the theodolite. Its because

it measures the angle of the building from the ground until to the flagpole on its top portion. This

develop the skills of the student in measuring the height of the building to the flagpole usingtrigonometry.

In the field work I learned how to compute the height of an object using an angle and a

side. This is taught in basic mathematics, but is now applied in the field. By getting the included

angle of the vertical distance and the slope we can compute for the height of the desired object. In

the field we learned how to use a theodolite. We used the theodolite to get the included angle used

for solving the height of the object. In the field work.

For this fieldwork, I recommend to learn the value of patience because it is very hard to

measure the angle of elevation to the flagpole and to measure the height of the building to the

flagpole. And also because of the sunny weather that we had when we performed this fieldwork. I

also recommend to be accurate in measuring, because if the measurement is not that accurate, it

can lead to a large percent error. Some of the reasons of the human errors in measuring is the

incorrect way of using the instruments or carelessness in measuring.

I can now conclude that the key to perform the field work well is to have confidence of

working with ones party or group and to be fully responsible in the performance of the assigned

task. Be obedient and cooperate to each other to finish the job easily. We also have to be extra

careful in using the instruments and perform the experiment properly to acquire an accurate result.

Application:

The field work can be applied when getting a data about a building. Using the methods in

the field work we can compute the height of the building that we are going to get the dimension to

maintain or renovate.


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FINAL DATA SHEET

FIELD WORK 3 TAPING ON SLOPING GROUND

DATE: 11/5/15 GROUP NO.: 4

TIME:9:00-11:00AM LOCATION: Mapua North Parking

WEATHER: Sunny PROFESSOR:Engr. Balmoris

STATION ANGLE MEAN

ANGLE

HEIGHT OF

INSTRUMENT

MEAN HEIGHT

OF

INSTRUMENT

A

(TELESCOPE

NORMAL)

6755

675530

1.195 m

1.1965 mA

(TELESCOPE

INVERTED)

6756 1.198 m

1.`STATION ANGLE

MEAN

ANGLE

67

HEIGHT OF

INSTRUMENT

MEAN HEIGHT

OF

INSTRUMENT

B

(TELESCOPE

NORMAL)

6145

614630

1.14 m

1.1425 mB

(TELESCOPE

INVERTED)

6148 1.145 m

A. COMPUTATION

tan =

= t a n +

= (40.35) tan(22430") + 1.1965

= 16.364 + 1.1965 = 17. 56


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Sketch:

Leveling the theodolite

Sighting the top of the building to get

the angle

Determining the height of the remote point, but in this

case, the height of the building


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fieldwork 8 (2nd draft)

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