A pilot flying over the Gulf of Mexico sees an island at an angle of depression of 12 degrees. At this time the horizontal distance from the airplane to the island is 4,812 meters.

Question

What is the height of the plane to the nearest meter?

823 meters
823 meters

4455 meters
4455 meters

1215 meters
1215 meters

1023 meters

Answer 1

Let h be the height of the plane above the island.
We can form a right triangle with the angle of depression of 12 degrees and the horizontal distance from the airplane to the island of 4,812 meters.
Using trigonometry, we have:
tan(12°) = h / 4,812
h = 4,812 * tan(12°)
h ≈ 1023 meters
Therefore, the height of the plane is 1023 meters to the nearest meter.