Question

Suppose a plane is coming down for a landing at Detroit Metro Airport. The angle

of depression is 18°. The altitude of the plane is 250 m. How far is the plane
from landing on the runway?

Answer 1

Using the tangent of the angle of depression and the altitude of the plane, the horizontal distance from a plane to the runway can be calculated with trigonometry.

Step-by-step explanation:

The student has asked a question related to trigonometry, which is a branch of mathematics particularly useful in finding distances and angles in various situations, such as the descent of an airplane.

To find the horizontal distance from the plane to the runway, we can use the angle of depression and the altitude of the plane. We know the angle of depression is 18°, and the altitude is 250 m. Drawing this as a right-angled triangle, we see that the altitude forms the opposite side and the distance to the runway the adjacent side related to the angle of depression.

Using the tangent trigonometric function in which tan(θ) = opposite/adjacent, we can rearrange the formula to find the distance (adjacent) as follows: distance = altitude / tan(18°). Plugging in the altitude, distance = 250 m / tan(18°). Therefore, the distance to the runway where the plane will land is determined by this calculation.