Question

A hot-air balloon is floating above a straight road. To estimate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 16° and 18°. How high is the balloon? (Round your answer to one decimal place.)

Answer 1

We know that
tan(∅) = y/x; where y will be the height of the balloon and x will be the distance from the milestone marker.
The marker that is further away will produce a smaller angle of depression.
tan(18) = height / x
x = height / tan(18)

The second marker is x + 1 miles away:
tan(16) = height / x + 1; substituting x:
tan(16) = height / (height/tan(18) + 1)
tan(16) x [(height / tan(18) + 1] = height
0.88h + 0.29 = h
h = 2.42 miles