Question

A helicopter hovers 500 feet above a small island. The figure shows that the angle of depression from the helicopter to point p is 50. How far off the coast to the nearest foot is the island.

Answer 1

In the problem, we were asked to find the distance from the base towards the island. First, we need to calculate for theta. So, 90-50 = 40°
Remember mnemonics, SOH CAH TOA. Since given is the angle and the altitude, we are going to use the tangent function.
tan40° = d/500
= 419.54 or approximately 420 feet.
The island is 420 feet away from the location underneath the helicopter.