Bob is driving along a straight and level road toward a mountain. At some point on his trip, he measures the angle of elevation to the top of the mountain and finds it to be 25°11'. Find the height of the mountain to the nearest foot if Bob is 19,427.5 feet from the center of the mountain at the base.

Question

10-04-2017
Mathematics

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Bob is driving along a straight and level road toward a mountain. At some point on his trip, he measures the angle of elevation to the top of the mountain and finds it to be 25°11'. Find the height of the mountain to the nearest foot if Bob is 19,427.5 feet from the center of the mountain at the base.

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Luv2Teach Luv2Teach · Answer 1 · 2017-04-12T01:59:32+02:00

You should know how to convert from minutes to degrees(?) if you are doing this problem. 11 minutes is equal to .1833 degrees, so the angle in degrees only (no minutes) is 25.1833 degrees. You have your angle now and you also have the measurement of the base leg. So to find the height of the mountain, use the tan ratio: tan(25.1833) = x/19427.5. Solving for x you get 19427.5tan(25.1833) = x, and that x = 9134.97 feet or, to the nearest foot, 9135 feet.