Question

An airplane over the pacific sights an atoll at a 17 degree angle of depression . If the plane is 485 m above the water, how many Km is it from a point 485 m directly above the center of the atoll.

Answer 1

tanα=h/d where h=height of the plane and d is the distance from plane to a point above the atoll.

d=h/tanα but this would be in meters and we need kilometers so

d=(h/tanα)(km/1000m)

d=h/(1000tanα), we are given that α=17 and h=485 then:

d=485/(1000tan17)

d≈1.586km (to the nearest thousandth of a km or to nearest meter)