SOLUTION: 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 14�52'. When t

Question 1014765: 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 14�52'. When the boat stops, the angle of depression is 45�10'. 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 by Boreal(15235) (Show Source): You can put this solution on YOUR website!
You have to draw this to have any chance to solve it.
The angle from the boat to the top of the lighthouse is 14d52m by alternate interior angles. The tangent of that is 200/x, where x is the first distance.
x tangent 14d52m equals 200
200/tangent 14d52 m =x
x=753.4189'
In the same fashion
200/tangent 45d10' is the final distance. That is 198.84 feet away.
If you do this all without rounding, it will be 554.58 feet (753.42-198.84) the boat moved.
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