Question

A balloon flying at 3000 feet above the ocean measures the angles of depression of each end of an island directly in front of the balloon to be 75.8° and 15.6°. What is the length of the island to the nearest tenth of a mile?

Answer 1

The length of the island will be given as follows:
tan θ=opposite/adjacent
thus:
tan75.8= 3000/a1
a1=3000tan75.8
a1=11855.885 ft

also:
tan15.6=3000/a2
a2=3000tan15.6
a2=837.62 ft
Thus the length of the island will be:
11855.885-837.615
=11,018.24 ft