Question

Question 4 (Essay Worth 3 points)

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is 17°31'. When the boat stops, the angle of depression is 46°41'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

Answer 1

445.10 feet to the nearest hundredth.

Explanation:

First work out the distance of the boat from the lighthouse when the angle of depression was 17°31':

tan 17°31' = 200 / x where x is the distance.

x = 200 / tan 17°31'

= 633.676 feet.

Now do the a similar calculation to find the distance at the second reading:

tan 46°41' = 200 / x

x = 200 / tan 46°41'

= 188.580 feet

Therefor the distance the boat travelled

= 633.676 - 188.580

= 445.10 feet.