Question

A helicopter hovers 550 feet above a small island. The figure shows that the angle of depression from the helicopter to point p is 43°. How far off the coast, to the nearest foot, is the island? (Round the answer to the nearest whole number.)

Answer 1

The angle of depression and angle P are alternate interior angles, then:

∠P = 43°

By definition:

tan(angle) = opposite/adjacent

In this case,

tan(43°) = 550/d

d = 550/tan(43°)

d = 590 ft