Angle of Depression

Question

The angle of depression from a boat to a treasure chest is 37°. The distance between the boat and the treasure is 800 ft. About how far below the surface of the water is the object? Round your answer to the nearest tenth.

Answer 1

The angle of elevation between the treasure and the boat is equal to the angle of depression = 37.

The height of the boat relative to the treasure is the opposite side to the angle of elevation and the 800 feet is the hypotenuse of the right triangle formed by the boat and the treasure.

So sin(37) = height / 800

800 sin(37) = height

height = 481.5 feet