An airplane pilot over the Pacific sights an atoll at an angle of depression of 7°. At this time, the horizontal distance from the airplane to the atoll is 3,729 meters.

Question

Triangle with depression of 7 degrees

What is the height of the plane to the nearest meter?
(1 point)
Responses

458 meters
458 meters

454 meters
454 meters

3,667 meters
3,667 meters

3,701 meters

Answer 1

To find the height of the plane, we can use trigonometry.

Let h be the height of the plane.

In the triangle formed by the horizontal distance (3,729 meters), the height of the plane (h), and the angle of depression (7 degrees), we have:

tan(7 degrees) = h / 3,729

Simplifying the equation, we have:

h = tan(7 degrees) * 3,729

Using a calculator, we can find:

h ≈ 458 meters.

So, the height of the plane to the nearest meter is 458 meters.