An observer at the top of a 60 m lighthouse sights two boats approaching, one behind the other.?

Question

An observer at the top of a 60 m lighthouse sights two boats approaching, one behind the other. The angles of depression of the boats are 38 degrees and 23 degrees. Find the distance between the boats to the nearest meter. Show all work to support your answer.

Answer 1

boat 1 (38 deg):

Range 1 = 60/tan(38 deg)=76.796 m

boat 2 (22 deg)

Range 2 = 60/tan(22 deg) = 141.351 m

The difference is 64.55 m = 65 m.

I also checked using a scale drawing.

Answer 2

I guess you mean that the angle of depression is the angle from the horizontal, downward. This angle is the same as the angle from the horizontal upwards, from the boat to the top of the tower.

So the distances are given by:
d*tan(angle) = 60
d = 60/tan(angle)

So the two distances are:
38 degrees: 76.8 m
23 degrees: 141.35 m

The difference between them is: 141.35 - 76.8 = 64.55
= 65 m

Answer 3

The distance between the two:

=60tan38 - 60tan23
=46.9 - 25.5
=21.4