Question 978518: 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. (3 points)
Answer by josgarithmetic(39625)   (Show Source):
You can put this solution on YOUR website! Examples like this, of this same form, are asked on occasion. Try drawing this:
A base segment, horizontally. From the right endpoint, make a vertical segment, y.
Pick an intermediate point on the base and draw a segment from it to the top point of the light house. Call the angle beta, and b is distance from this point on the base to the bottom of the light house.
Draw the segment from the left endpoint of the base to the top of the light house. The angle at that left base endpoint will be alpha. Let d be the distance from left base endpoint to the intermediate base endpoint.
Drawing that through the code for the algebra dot com system is very difficult and would take too long to form. You have alpha is 17 degrees 31 minutes, and beta is 46 degrees 41 minutes. You want to solve for d which is distance from left endpoint of base to the intermediate point of where the boat stopped.
y is known since here given y=200, alpha and beta are known. b and d are both unknown but you will be able to solve for either or both of them, having the two equations.
Starting with the alpha equation,
Working with the beta equation,  , and then substituting this in the d & alpha equation,
 , which you can adjust in form in whatever way you are most comfortable, before obviously substituting the known or given values.
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