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? (1 point) Responses 3,701 meters 3,701 meters 3,667 meters 3,667 meters 458 meters 458 meters 454 meters
The height of the airplane can be found using trigonometry. In this case, the tangent of the angle of depression is equal to the opposite side (height of the plane) divided by the adjacent side (horizontal distance to the atoll).
Let x be the height of the plane. We can set up the equation as follows:
tan(7°) = x / 3729
Using a calculator, we find that tan(7°) ≈ 0.1228.
Therefore, x ≈ 3729 * 0.1228 ≈ 458 meters.
So, the height of the plane is 458 meters. The closest response listed is 458 meters.