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30 Points please help!! Please explain 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.

Answer :

Initial: 200 feet = opp. side
Angle = 17.31, adj. Side = a
So tan (17.31) = opp. Side / adj. Side
tan (17.31) = 200 / a
--> a = 200/tan17.31 = 641.73
When stopped: adj. Still = a
Opp. Side still = 200, angle = 46.41
tan46.41 = 200 / a
--> a = 200/tan46.41 = 190.39
Now subtract those two distances to get the distance traveled from initial to when it stopped:
641.73 - 190.39 = 451.34 feet

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