An airplane approaches a runway at a 3 degree angle of depresssion. If the plane is flying at 30,000 ft., find the ground distance from the airport to the point directly below the plane when the pilot begins the descent. Round your answer to the nearest foot.

To find the ground distance from the airport to the point directly below the plane when the pilot begins the descent, we can use trigonometry.

Let's denote the ground distance we need to find as "x". We are given that the airplane is flying at a height of 30,000 ft and at a 3 degree angle of depression. This means that the angle between the horizontal ground and the line of sight from the plane to the point directly below is 3 degrees.

We can use the tangent function to find the ratio between the height and the ground distance:

tan(angle) = opposite/adjacent,

where the opposite side is the height of the plane (30,000 ft) and the adjacent side is the ground distance (x).

Plugging in the values we know, we get:
tan(3) = 30,000/x.

To solve for x, we can rearrange the equation as follows:

x = 30,000 / tan(3).

Using a scientific calculator, we find that the tangent of 3 degrees is approximately 0.0524.

Substituting this value into our equation, we have:
x = 30,000 / 0.0524.

Evaluating this expression, we find that x is approximately 571,770 feet.

Rounding to the nearest foot, the ground distance from the airport to the point directly below the plane when the pilot begins the descent is 571,770 feet.