Question

An observer from the top of a lighthouse 370 feet above sea level sees two sailboats in the water. The angles of depression to the boats are 12 degrees and 10 degrees. How far apart are the boats, to the nearest foot?

Answer 1

Answer:the sailboats are 358 feet apart.

Explanation:

The diagram of the triangle representing the situation is shown in the attached photo.

B represents the position of the lighthouse.

D represents the position of the first sailboat.

C represents the position of the second sailboat.

x represents the distance between the two sailboats

We would apply trigonometric ratio

Tan # = opposite/adjacent

For triangle ABD,

Tan 12 = 370/AD

AD = 370/Tan 12 = 370/0.2126 = 1740.357 feet

For triangle ABC,

Tan 10 = 370/AC

AD = 370/Tan 10 = 370/0.1763 = 2098.695 feet

x = AC - AD = 2098.695 - 1740.357 = 358 feet