Question

A plane is a horizontal distance of 15,840 feet away from an airport. The plane has an angle of depression of 48°. What is the altitude of the plane? Round your answer to the nearest foot.

a) 10,817 feet
b) 12,524 feet
c) 14,290 feet
d) 15,840 feet

Answer 1

The altitude of the plane is approximately 12,523 feet.

Step-by-step explanation:

To find the altitude of the plane, we can use trigonometry and the concept of angle of depression. Since we know the distance from the plane to the airport is 15,840 feet and the angle of depression is 48°, we can use the tangent function to find the altitude. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the altitude and the adjacent side is the distance to the airport. Therefore, we have:

Altitude = Distance * tan(angle)

Plugging in the values, we get:
Altitude = 15,840 * tan(48°)

Using a calculator, the altitude is approximately 12,523 feet.