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What is the height of the hill if the elevation of a hill at a place due east of it is 39 degrees at a place B due south of A the elevation is 27 degrees and the distance from A to B is 500m?
Shennyboy
It is not clear from the question where the point A is. This answer assumes that A is the point to the East of the hill.
Suppose the height of the hill is h metres. Suppose O is the point, on ground level, under the apex of the hill.
Then tan(39) = h/OA so that OA = h/tan(39)
Also tan(27) = h/OB so that OB = h/tan(27)
Now, triangle OAB has a right angle at A,
so by Pythagoras, OB2 = OA2 + AB2
Therefore h2/tan2(27) = h2/tan2(39) + 5002
that is h2/0.2596 = h2/0.6558 + 250000
so that 2.3269h2 = 250000
h2 = 107441
h = 327.8 metres.
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∙ 10y ago
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