.

Introduction:
A civil engineer should know how to use theodolite to measure width or height of building or something else . In the last surveying lab we used the theodolite instrument and we use it for measuring the angles vertical and horizontal that the civil engineer could need to do some subjects and its simple and easy to use

Method:

During this experiment we’ll locate 2 points and measure the distance between them and then we’ll but the theodolite on each point and measure the horizontal angles with a building that in our view and then measure its vertical angles from the top and the bottom of the building with the horizon and our objective from this experiment is to Get familiar with theodolite instrument and know the basics of it and what it used for and learn how to do centering and levelling to the instrument and we increase our ability of making reads and measuring angels ( vertical and horizontal ) .

Equipment:
1- Theodolite instrument 2- Calculator 3- Tripod 4- Ranging poles

Results & Calculations:
 Data (with graph)  Horizontal angel

AB = 4.9 M

We set the theodolite at point A and we measure angels α1 and α2 after levelling and centering the theodolite And then we move the instrument to point B to measure angels α3 and α4 By theodolite the angels will be like the following :

α 1 = 19.1 gon = 17.19° α 2 = 73.22 gon = 65.89° α 3 = 21.59 gon = 19.43° α 4 =113.53 gon = 102.18°

- α 5 = 180° - (α 1+ α 2+ α 4) - α 5 = 180° - (185.26) - = -5.26 = 5.26°

- α 6 = 180 – (α 3 + α 4 + α 2) - α 6 = 180 – (187.5) - = -7.5 = 7.5°

using the tape we measure length of AB and by calculation we can measure A'B'

B'

B

A

- AB’ / (sin (α 4 + α 3)) = AB / sin α 6 AB’ = (AB * sin (α 4 + α 3))/ sin α 6 AB’ = 31.97 M

A'

B

A

- BA’ / (sin (α 1 + α 2)) = AB / sin α 5 BA’ = (AB * sin (α 1 + α 2))/ sin α 5 BA’ = 53.06 M

 Measuring vertical angel

We use the tape to measure the length of AB and by the theodolite instrument we can measure the vertical angels α 1 = 12.924 gon = 11.63° α 2 = 4.864 gon = 4.378° AB = 27.20 m CD = 27.20 * tan α 1 DB = 27.20 * tan α 2 CD = 5.59 DB = 2.08

The elevation of the building is 5.59+2.08 = 7.67 m (approx.)

Discussion:
We need to be careful when using the theodolite to get the real and true reading and as we saw we can find distances by the theodolite by some equation such as sine and cosine laws Some errors may happened such as : -Error in levelling the theodolite and centering -From the calculation the value is close to true value. -Take wrong readings -Moving the theodolite will give us falls reading

Conclusion:
1- It is easy to find distances by the theodolite 2- Levelling and centering is the main source of errors plus to human error. 3- We can measure heights by theodolite