Question

A little girl is watching planes take off of the runway from a building's rooftop 40 meters away from the airport. If the height of the building is 400 meters and the girl snaps a photo of a plane at a 24º angle of elevation, what is the altitude, or vertical height, of the plane when the photo is taken?

Answer 1

h = 417.81 meters

The altitude of the plane is 417.81 meters

Explanation:

given;

The initial height of the girl h0 = 400 m

Horizontal distance from the airport d = 40 m

Angle of elevation of the plane ∅= 24°

The altitude of the plane when the picture was taken is equal to initial height of the girl plus the elevation height.

h = he + h0

And he (elevation height) can be derived as;

he = dtan∅

he = 40tan24°

Substituting into the equation;

h = 40tan24° + 400

h = 417.81 meters

The altitude of the plane is 417.81 meters