Question

Can someone pleaseee helppp 30 pointsss

An observer at the top of a 50 m lighthouse sights two ships approaching, one behind the other.
The angles of depression of the ships are 36° and 25°. Find the distance between the ships to the nearest meter.

Answer 1

Let d1 be the distance of the first boat to the lighthouse. Then

tan(36) = 50/d1

or

d1 = 50/tan(36) ≈ 68.819096023558677

Let d2 be the distance of the second boat to the lighthouse. Then

tan(25) = 50/d2

or

d2= 50/tan(25) ≈ 107.225346025477931

107.225346025477931 - 68.819096023558677 ≈ 38 (to the nearest meter)