Question 403450: Last problem I'm stuck on...please help!!
A motorist, traveling along a level highway at a speed of 60 km/h directly toward a mountain, observes that between 1:00 PM and 1:10 PM, the angle of elevation to the top of the mountain changes from 10 degrees to 70 degrees. Approximate the height of the mountain.
Thanks!!!
Answer by nerdybill(7384)   (Show Source):
You can put this solution on YOUR website! A motorist, traveling along a level highway at a speed of 60 km/h directly toward a mountain, observes that between 1:00 PM and 1:10 PM, the angle of elevation to the top of the mountain changes from 10 degrees to 70 degrees. Approximate the height of the mountain.
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Draw the diagram -- it'll help you "see" the solution.
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distance traveled in 10 minutes = 10 km
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Let x = height of mountain
and y = distance of car at 1:10 and the point perpendicular to peak
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tan 10 = x/(10+y)
tan 70 = x/y
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y = x/tan70
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tan 10 = x/(10 + x/tan70)
tan10/tan70 = x/(10tan70 + x)
tan10(10tan70 + x) = xtan70
10tan10tan70 + xtan10 = xtan70
10tan10tan70 = xtan70 - xtan10
10tan10tan70 = x(tan70-tan10)
(10tan10tan70)/(tan70-tan10) = x
1.88 km = x
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