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?

Answer 1

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.