Question

A surveyor is standing 30 feet from the base of a tall building. The surveyor measures the angle of elevation from the ground to the top of the building to be 65°. Find the height h of the building to the nearest foot.

Answer 1

We will use the tangent ratio since we have the adjacent side to the 65 degrees and we need to find the opposite side to the 65 degrees.

Tan α = opp/adj
Tan 65 = x/30
To solve, multiply both sides by 30.
30 Tan65 = x
x = 64 ft