Asked by William320
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?
Answers
Answered by
Reiny
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
(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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.