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?
To find the height of the plane, we can use trigonometry and the tangent function.
Let's assume that the height of the plane is h meters.
In a right triangle formed by the plane, the island, and the horizontal distance, the angle of depression (angle between the horizontal line and the line of sight to the island) is 12 degrees.
Using the tangent function, we can write:
tan(12 degrees) = h / 4812 meters
Rearranging the equation to solve for h:
h = tan(12 degrees) * 4812 meters
Using a calculator, we find:
h ≈ 1112.9 meters
Therefore, the height of the plane is approximately 1112 meters to the nearest meter.