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?
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°