To find the height of a tower a survivor sets up his theodolite 120 meter from the base of the tower. He finds that the angle of elevation to the top of the tower is 30° . If the instrument is 4.5 meter from the ground. What is the height of the tower?
We can use trigonometry to solve this problem.
Let's assume the height of the tower is H meters.
From the given information, we have:
Distance from the theodolite to the base of the tower = 120 meters
Angle of elevation to the top of the tower = 30°
Height of the theodolite = 4.5 meters
Now, let's draw a diagram to visualize the problem:
T
/|
H / |
/ |
/ |120
/ |
/30 |
/______|
4.5
Using the angle of elevation, we can determine the length of the opposite side (H) as follows:
tan(30°) = H / 120
H = 120 * tan(30°)
Now, let's calculate the height of the tower:
H = 120 * tan(30°)
H = 120 * 0.5774
H ≈ 69.29 meters
Therefore, the height of the tower is approximately 69.29 meters.