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.
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
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.