Question

The angle of depression of a buoy from a point on a lighthouse 120 feet above the water's surface is 10 degrees. Find the distance from the lighthouse to the buoy. Leave answer with two decimal places.

Answer 1

680. 55 feets

Explanation:

From the diagram, distance from lighthouse to buoy = x

Angle from top of lighthouse to buoy = (90 - 10) = 80°

Using the trigonometric relation :

Tanθ = opposite / Adjacent

Opposite = x

Adjacent = 120

Tan 80 = x / 120

5.6712818 = x / 120

x = 5.6712818 * 120

x = 680. 55 feets