Question

An airplane flying at a given altitude begins its descent directly above a ground marker that is 20.42 miles from the runway. If the glide angle of the airplane to the ground is 30 degrees, how far did the airliner travel in the air from the point of descent until the plane touched ground? Round your answer to the nearest tenth mile.

Answer 1

40.8 miles.

Explanation:

To solve this problem, we need to know the distance that the airplane traveled in the air from the point of descent until it touched the ground. This distance is determined by the glide angle and the altitude of the airplane.

In general, the distance traveled in the air is equal to the altitude of the airplane divided by the sine of the glide angle. In this case, we are given the altitude and the glide angle, so we can calculate the distance traveled in the air as follows:

Distance = Altitude / sin(glide angle)

Plugging in the values from the problem, we have:

Distance = 20.42 miles / sin(30 degrees)

The sine of 30 degrees is 0.5, so the distance traveled in the air is:

Distance = 20.42 miles / 0.5

This simplifies to:

Distance = 40.84 miles

Rounded to the nearest tenth mile, the distance traveled in the air is 40.8 miles. This is the answer to the problem.