Question

From a hot air balloon, the angle between a radio antenna straight below and the base of the library downtown is 57°, as shown below. If the distance between the radio antenna and the library is 1.3mls, how many miles high is the balloon?

Answer 1

As you can see in the diagram, the figure formed is a right triangle. Hence, we can use the trigonometric functions. Let's assign x for the altitude of the balloon to be determined. 

tan 57 = opposite side/adjacent side
tan 57 = 1.3/x
x = 1.3/tan57
x = 0.84 miles

Thus, the hot balloon is 0.84 miles high.