Question

An observer in a lighthouse 60 ft above sea level finds that the angle of depression of a small boat on the water is 4°. Find the distance of the boat from the base of the lighthouse.

Answer 1

Given:

height of lighthouse = 60 ft

angle of depression = 4°

To find:

distance of the boat =?

Step-by-step explanation:

• An observer is on a lighthouse of a height 60 ft above sea level.
• The boat is floating in the seawater.
• The angle of depression of a small boat on the water is 4°.
• Now, we have to find that, the distance of the boat from the base of the lighthouse.
• Let x be that disance.

• From fig

       tan 4 = $\displaystyle \frac{60}{x}$

       x = 858.04 ft

• Hence, the distance of the boat from the base of the lighthouse is 858.04 ft.

Refer to the following attachement: