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. What is the height of the plane to the nearest meter
To find the height of the plane, we need to use trigonometry.
Let h be the height of the plane above the atoll.
We can form a right triangle with the height of the plane, the horizontal distance to the atoll, and the line of sight from the plane to the atoll.
We know the angle of depression is 7°, so the angle at the top of the triangle (opposite the height of the plane) is also 7°.
We can use the tangent function to find the height of the plane:
tan(7°) = h / 3,729
h = 3,729 * tan(7°)
h ≈ 453 meters
Therefore, the height of the plane above the atoll is approximately 453 meters.