SOLUTION: A bush walker estimates the angle of elevation to the top of the hill to be 22 degrees. After walking 700 metres closer to the hill, the angle of elevation to the top of the hill b

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Question 1173655: A bush walker estimates the angle of elevation to the top of the hill to be 22 degrees. After walking 700 metres closer to the hill, the angle of elevation to the top of the hill becomes 38 degrees. Determine the height of the hill.
Answer by VFBundy(438) About Me  (Show Source):
You can put this solution on YOUR website!


Based on the information given, I have set up the problem.

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Use the Law of Sines on the left triangle to find 'a':

a%2Fsin+22 = 700%2Fsin+16

a%2F0.3746 = 700%2F0.2756

0.2756a = 700%280.3746%29

0.2756a = 262.22

a = 951.45

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Use the Law of Sines on the right triangle to find 'x':

x%2Fsin+38 = 951.45%2Fsin+90

x%2F0.6157 = 951.45%2F1

x = 951.45%280.6157%29

x = 585.81

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The height of the hill is 585.81 metres.