Posted by William320 on Thursday, August 1, 2013 at 11:42am.
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  Reiny, Thursday, August 1, 2013 at 12:53pm
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 rightangled triangle, PBQ
sin24 = PQ/AP
PQ = APsin24 = 2.0188 miles high
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