30 pointsexplain too! 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.

445.10 feet to the nearest hundredth.

Step-by-step 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.