Question 1129202: A driver in a car traveling along a straight level road at 62 miles per hour sees a mountain in the distance. The driver determines that the angle of elevation to the top of mountain to be 19∘22′. After 20 minutes, the driver determines the angle of elevation to the top of the mountain to be 34∘25′. Calculate the height of the mountain to the nearest foot.
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! In 20 minutes the car travels 62/3 is approximately 20.67 miles
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22' = 22/60 is approximately 0.37 degrees
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25' = 25/60 is approximately 0.42 degrees
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tan 19.37 degrees = h/(x+20.67), where h is the height of the mountain, x is the horizontal distance from the mountain to the car after it has traveled 20 minutes
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h = 0.35(x+20.67)
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1) 0.35x +7.23 = h
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tan 34.42 = h/x
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2) 0.69x = h
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solve equation 2 for x
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x = h/0.69
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substitute for x in equation 1
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0.35(h/0.69) +7.23 = h
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multiply both sides of = by 0.69
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0.35h +4.99 = 0.69h
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0.34h = 4.99
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h = 4.99/0.34 is approximately 14.68 miles
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height of the mountain is 14.68 * 5280 is approximately 77,510 feet
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