A model airplane 50 feet above the ground is flying away from an observer. Find the angle of elevation theta of the plane as a function of the distance from the observer to the plane. What is theta when the plane is 200 feet from the observer?

Answer 1

You are basically interested in the length of the hypotenuse of
a right-angled triangle with a height of 50 and a base angle of θ

so sinθ = 50/h, where h is the hypotenuse
h = 50/sinθ or if you want: y = 50 cscθ
θ = sin^-1 (50/h) or θ = arcsin (50/h)

when h = 200,
sinθ = 50/200 = .25
θ = appr 14.5°