A helicopter hovers 1250 feet
above a small island. The figure
shows that the angle of
depression from the helicopter
to point P is 47º. How far off
the coast, to the nearest foot, is
the island?

Create a right triangle.

The height of the leg will be 1250 feet. We are given an angle of depression of 47°, so we can draw an imaginary line parallel to the base of the triangle.

By the AIA Theorem, the angle of the bottom right side of the right triangle will be 47 degrees.

We want to find the distance between the coast and the island. In other words, find the length of the base of the triangle. We can do so with trigonometric ratios.

tan47 = 1250/x

x = 1166.