Question

A lighthouse is 90 feet above sea level. The angle of depression from the top of the lighthouse to the center of the rock is 35 degrees, and the angle of depression to the swimmer is 45 degrees. Find the distance between the center of the rock and the swimmer.

Answer 1

notice the picture below

so.... the angle of depression, is above in dashed lines.... however, the angle of depression, is identical to the angle of elevation from the water, since, both angles are "alternate interior" angles

now, using the 45-45-90 rule, then we know the swimmer is 90 feet from the lighthouse, then just use the tangent ratio to get "x"