The angles of elevation of a balloon from two points A and B on level ground are 24°10' and 47°40'

Question

The angles of elevation of a balloon from two points A and B on level ground are 24°10' and 47°40', respectively. As shown in the figure, points A and B are a = 7.5. miles apart, and the balloon is between the points, in the same vertical plane. Approximate the height of the balloon above the ground. (Round your answer to one decimal place.)

Answer 1

h represents the height of the balloon

C is a point on the ground directly below the balloon

BC = 7.5 - AC

h / AC = tan 24° 10'

h = AC tan 24° 10'

h / tan 24° 10' = AC

h / BC = tan 47° 40'

h = BC tan 47° 40'

h / tan 47° 40' = BC

h / tan 47° 40' = 7.5 - AC

h / tan 47° 40' = 7.5 - [h / tan 24° 10']

Can you solve for h and answer?