Question

The look-out point of a lighthouse is 50 feet above sea level. A woman observes a boat in the water from the look-out point. The angle of depression to the boat in the water is 20°.

What is the distance from the base of the light house to the boat in the water?

Answer 1

137.373871

Rounded to the 10th place

137.4

Rounded to the whole number

137

Explanation:

There are a few methods for solving this type of problem. Please view the images I have provided. I gave two methods for solving this problem.

Answer 2

137.4 feet

Explanation:

Consider the attached diagram. The given angle of depression from the lighthouse to the boat is the same as the angle of elevation from the boat to the lighthouse. The trig relationship for tangent tells you ...

... tan(20°) = opposite/adjacent = AL/AB = 50'/AB

Solving for AB, we get

... AB = 50'/tan(20°) ≈ 50'/0.36397

... AB ≈ 137.4'