A plane flying at an altitude of 10,000 feet begins descending when the end of the runway is 50,000 feet from a point on the ground directly below the plane. Find the measure of the angle of descent (depression) to the nearest degree.
To find the measure of the angle of descent (depression), we can use trigonometry. In this case, we can use the tangent function.
Let's define the given information:
- The altitude of the plane is 10,000 feet.
- The distance from the end of the runway to a point on the ground directly below the plane is 50,000 feet.
We can create a right triangle with the altitude as the vertical leg, the distance as the horizontal leg, and the angle of depression as the angle opposite the altitude.
Using the tangent function, we have:
tangent(angle) = opposite / adjacent.
In this case, the opposite side is the altitude, and the adjacent side is the distance from the end of the runway to the point on the ground.
tangent(angle) = 10,000 / 50,000.
To find the angle, we can take the inverse tangent (also known as arctan) of both sides:
angle = arctan(10,000 / 50,000).
Using a calculator, we can find that arctan(10,000 / 50,000) is approximately 11.31 degrees.
Therefore, the measure of the angle of descent (depression), to the nearest degree, is 11 degrees.
To find the measure of the angle of descent (depression), we can use trigonometry.
Let's consider a right triangle, where the vertical leg represents the altitude of the plane (10,000 feet) and the horizontal leg represents the distance from the plane to the point on the ground (50,000 feet).
We can use the tangent function to find the angle of descent (depression):
tangent(angle) = vertical leg / horizontal leg
tangent(angle) = 10,000 / 50,000
angle ≈ arctan(0.2)
Using a calculator, we find that the angle ≈ 11.3 degrees.
Therefore, the measure of the angle of descent (depression) is approximately 11 degrees to the nearest degree.