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?

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