heigth of a weather balloon

Question

2 weather observation stations are 7 miles apart. A weather balloon is located between the stations. From station 1, the angle of elevation to the weather baloon is 33 degrees. from station 2, the angle of elevation from the station to the baloon is 52 degrees. Find the altitude of the balloon to the nearest tenth of a mile. 

Answer 1

Draw and label a diagram. Station 1 is A, station 2 is B, the balloon is C, the point directly beneath the balloon is D.

 

m∠ACB = 95°, m∠ADC = m∠BDC = 90°

 

Use the Law of Sines

sin A / a = sin B / b = sin C / c

to determine the length of either AC or BC (doesn't matter which)

 

Once AC (or BC) is determined use Law of Sines to determine DC.