Question

Nicole spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7225 feet. Nicole initially measures an angle of elevation of 15 ∘ ∘ to the plane at point � A. At some later time, she measures an angle of elevation of 33 ∘ ∘ to the plane at point � B. Find the distance the plane traveled from point � A to point � B. Round your answer to the nearest tenth of a foot if necessary.

Answer 1

15838.5 ft

Explanation:

You want the distance an airplane travels at an altitude of 7225 feet from point A at an angle of elevation of 15° to point B at an angle of elevation of 33° on the line in the direction toward the observer.

Tangent

The tangent function relates the angle of elevation to the height and horizontal distance like this:

Tan = Opposite / Adjacent

tan(angle of elevation) = height/(horizontal distance)

The difference in horizontal distances is ...

horizontal distance = height/tan(angle of elevation)

AB = 7225/tan(15°) -7225/tan(33°)

AB = 26964.067 -11125.524 ≈ 15838.5

The plane traveled about 15,838.5 feet from point A to point B.

<95141404393>