Question 976691: To measure the height of a lighthouse, two sightings are taken, one 50 feet directly behind the other. If the first angle of elevation is 53* and the second is 48*, what is the height of the lighthouse. Find the exact answer and then use the calculator to approximate the answer, rounded to the nearest foot.
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! Draw the description:
A base segment; at the right endpoint, draw a vertical segment to represent the lighthouse. Draw a segment to connect the base's left endpoint to the top of the lighthouse and label the angle of elevation 48 degrees. Someplace on the base segment, pick another point and draw a segment connecting this point to the top of the lighthouse, and label the angle of elevation 53 degrees.
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This is an outer right triangle and a smaller right triangle, both sharing the tallness of the lighthouse and a common right angle at the base point at the bottom of the lighthouse.
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Let d be the distance from the nearer reference point between the lighthouse along the base segment. This means the base length from left endpoint to the right endpoint is d+50.
Let y be the height or tallness of the lighthouse.
Study the diagram you just made as described, and you should be able to form a system of equations like this:
That is two equations in two unknown variables, and you can solve the system for both variables; and you are most interested in finishing with the value for y.
Report if you have (any) trouble handling the algebra. You should have no trouble.
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Not showing all the steps for the algebra here, I found
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