SOLUTION: Two observers on the ground are 2000m apart. Observer A measures the angle of elevation of a hot air balloon at his right to be 37 degrees. Observer B, on the other hand, measures

Algebra ->  Trigonometry-basics -> SOLUTION: Two observers on the ground are 2000m apart. Observer A measures the angle of elevation of a hot air balloon at his right to be 37 degrees. Observer B, on the other hand, measures       Log On


   

Question 1124013: Two observers on the ground are 2000m apart. Observer A measures the angle of elevation of a hot air balloon at his right to be 37 degrees. Observer B, on the other hand, measures the angle of elevation of the air balloon at his left to be 15 degrees. Find the altitude of the hot air balloon.
Answer by rothauserc(4718) About Me  (Show Source):
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37 + 15 = 52 degrees
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180 - 52 = 128
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label balloon point O, then angle AOB is 128 degrees
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use law of sines to find the lengths of AO and OB
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2000/sin(128) = OB/sin(37)
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OB * sin(128) = 2000 * sin(37)
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OB = 2000 * sin(37) / sin(128) = 1527.43 m
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AO = 2000 * sin(15) / sin(128) = 656.89 m
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use Heron's formula to find area of triangle AOB
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s = (2000 + 1527.43 + 656.89) / 2 = 2092.16
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Area of AOB = square root(2092.16 * (2092.16 -1527.43) * (2092.16 - 656.89) * (2092.16 - 2000)) = 395326.49
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(1/2) * base * height = Area of AOB
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(1/2) * 2000 * height = 395326.49
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height = (2 * 395326.49) / 2000 = 395.33
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height of balloon is 395.33 m
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