SOLUTION: The angular elevation of a hill at a place P due south of it is 37 degrees and at a place Q due west of P the elevation is 23 degrees. If the distance from P to Q is 3km, find the
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-> SOLUTION: The angular elevation of a hill at a place P due south of it is 37 degrees and at a place Q due west of P the elevation is 23 degrees. If the distance from P to Q is 3km, find the
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Question 1140095: The angular elevation of a hill at a place P due south of it is 37 degrees and at a place Q due west of P the elevation is 23 degrees. If the distance from P to Q is 3km, find the height of the hill, to the nearest 10 metres Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! A due south bearing is 180 degrees
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A due west bearing is 270 degrees
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Let x be the height of the hill
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we have two right triangles, let b1 and b2 be the bases of the two triangles
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tan(37) = x/b1
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b1 = x/tan(37)
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similarly
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b2 = x/tan(23)
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we have a triangle with two sides equal to x/tan(37) and x/tan(23) and the angle between them is 270 - 180 = 90 degrees
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ues Pythagorean Theorem
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(x/tan(37))^2 + (x/tan(23))^2 = 3^2
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x^2/0.7536^2 + x^2/0.4245^2 = 9
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x^2/0.5679 + x^2/0.1802 = 9
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9/x^2 = 1/0.5679 +1/0.1802 = 7.3103
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x^2 = 9/7.3103 = 1.2311
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x = 1.1095km = 1109.5m is approximately 1110m
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