A person in a balloon which is 2,000 feet above the airport finds that the angle of depression to a ship out at sea is 21°. Find the horizontal distance between the balloon and the ship.

The horizontal distance is given by the formula:

tan θ=opposite/adjacent

where:

θ=21

opposite=2000 ft

adjacent=a

thus calculating for a we get:

tan 21=2000/a

thus

a=2000/tan 21

a=5210.18 ft

Answer: 5210.18 ft