Question 1124013
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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