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

Question

823 meters
4455 meters
1023 meters
1215 meters

Answer 1

To solve this problem, we can use trigonometry and the tangent function.

First, label the angle of depression as 12 degrees, the horizontal distance as 4,812 meters, and the height of the plane as h.

We can set up a right triangle with the angle of depression at the island. The side opposite the angle of depression is the height of the plane, and the side adjacent to the angle of depression is the horizontal distance.

Using the tangent function, we can set up the following equation:

tan(12 degrees) = h / 4,812 meters

To find the height of the plane, we can rearrange the equation and solve for h:

h = tan(12 degrees) * 4,812 meters

h ≈ 1023 meters

Therefore, the height of the plane is approximately 1023 meters to the nearest meter. So the correct answer is 1023 meters.