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 right-angled triangle, PBQ

sin24 = PQ/AP

PQ = APsin24 = 2.0188 miles high

## Answer This Question

## Related Questions

- differential calculus - ANGLE OF ELEVATION A balloon rises at a rate of 4 meters...
- math - A balloon rises at a rate of 3 meters per second from a point on the ...
- calculus : related rates - a balloon rises at a rate of 3 meters per second from...
- Calc - 2) A hot air balloon rising vertically is being tracked by an observer on...
- Math - a balloon is rising vertically at the rate of 2 m/s. an observer is ...
- Math - A hot air balloon is observed from two points A and B on the ground A and...
- Trig - A weather balloon is sighted between points A and B which are 5 miles ...
- Calculating distance(law of cosines) - Observers P and Q are located on the side...
- Calc - A balloon, 50 feet from an observer is rising at 20 ft/sec. At 5 sec ...
- Calculus Related Rates - A hot air balloon, 50 feet from an observer, is rising ...

More Related Questions