A helicopter hovers 630 feet above a small island. The angle of depression from the helicopter from point P is 47 degrees. How far off the coast, to the nearest foot, is the island?

Answer 1

Let the distance from the helicopter to the point where it is directly above point P on the island be x feet.

Since the angle of depression is 47 degrees:

tan(47) = 630/x

Solving for x:

x = 630 / tan(47)
x ≈ 569.43 feet

Therefore, the island is approximately 569 feet off the coast.