Question

A plane is flying within sight of an airport, at an elevation of 30,000 ft. The pilot would like to estimate the plane's distance to a point on the runway and finds that the angle of depression to that point is 24°. What is the distance of the plane from the point on the runway?

Answer 1

To calculate the distance from the plane to the runway, we use the angle of depression and the plane's altitude to form a right triangle. Using the tangent of the angle of depression, which is the same as the angle of elevation, we find that the distance equals the altitude divided by the tangent of the angle.

Step-by-step explanation:

To find the distance of the plane from the point on the runway, we can use trigonometry. The problem provides us with the angle of depression from the airplane to the runway, which is 24°, and the altitude of the airplane, which is 30,000 feet. The angle of depression is the same as the angle of elevation from the point on the ground to the airplane due to alternate interior angles created by a parallel line to the ground and a transversal (the line of sight from plane to ground).

Using this angle, we can form a right triangle with the altitude of the plane as one leg and the distance to the point on the runway as the hypotenuse. Using the tangent function, which is the ratio of the opposite side over the adjacent side in a right triangle, we have:

tangent(angle) = opposite/adjacent

With our given values:

tangent(24°) = 30,000 ft / distance

Therefore:

distance = 30,000 ft / tangent(24°)

After calculating this expression, we will have the distance from the plane to the point on the runway.