# Math

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A ground observer sights a weather balloon to the east at an angle of elevation of 15º. A second observer 3 miles to the east of the first also sights the balloon to the east at an angle of elevation of 24º. How high is the balloon?

• Math -

make a sketch, labeling the balloon P and the point directly below it on the ground as Q
(We have to find PQ)

Label the first observer as A and the second as B
AB = 3
angle PAB = 15° , angle PBQ = 24°

In triangle PAB,
angle A = 15, angle PBA = 156° , so angle APB = 9°

by the sine law:
AP/sin15 = 3/sin9
AP = 3sin15/sin9 = 4.963465... ( I stored in calculator's memory)

In the right-angled triangle, PBQ
sin24 = PQ/AP
PQ = APsin24 = 2.0188 miles high

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