To approach the runway, the pilot of a small plane, must begin at a 15 degree descent starting at a height of 2,530 feet above the ground. To the nearest tenth of a mile, how many miles from the runway is the plane at the start of this approach?

Question

To approach the runway, the pilot of a small plane, must begin at a 15 degree descent starting at a height of 2,530 feet above the ground. To the nearest tenth of a mile, how many miles from the runway is the plane at the start of this approach?

Answer 1

To find the distance from the runway at the start of the approach, we can use trigonometry. We can create a right triangle where the height of the plane above the ground is the opposite side, the distance from the runway is the hypotenuse, and the angle of descent is 15 degrees.

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

sin(15 degrees) = 2530 / distance from runway

Solving for the distance from the runway, we get:

distance from runway = 2530 / sin(15 degrees) ≈ 9546.2 feet

Converting feet to miles by dividing by 5280 (since 1 mile = 5280 feet), we get:

distance from runway ≈ 1.8 miles

Therefore, the plane is approximately 1.8 miles from the runway at the start of the approach.