Question

To find the height of a tower, a surveyor positions a transit that is 2 meters tall at a spot 35 meters from the base of the tower. She measures the angle of elevation to the top of the tower to be 37°. What is the height of the tower, to the nearest meter?

Answer 1

The answer to your question is 28.37 m

Explanation:

Data

height of the transit = 2 m

distance to the tower = 35 m

angle = 37°

Process

To solve this problem use trigonometric functions. The trigonometric function that relates the Opposite side and the adjacent side is tangent.

tan Ф = Opposite side / Adjacent side

-Solve for Opposite side

Opposite side = Adjacent side x tan Ф

1) Substitute values

Opposite side = 35 x tan 37°

2) Simplification

Opposite side = 35 x 0.7536

Opposite side = 26.37 m

3) Calculate the height of the tower.

Height = 26.37 + 2

= 28.37 m