From the top of a 214-ft lighthouse, the angle of depression to a ship in the ocean is 15°. How far is the ship from the base of the lighthouse?

Question

From the top of a 214-ft lighthouse, the angle of depression to a ship in the ocean is 15°. How far is the ship from the base of the lighthouse? 

distance = in feet

Answer 1

Draw and label a diagram.

d represents the distance from the base of the lighthouse.

tan 15° = 214 / d

d tan 15º = 214

d = 214 / tan 15º

d ≈ 214 / 0.267949

d ≈ 798.659

Answer 2

tan(15) = opposite/adjacent = x/214

x = 214tan(15) = 57.3 feet