Question

To approach the runway, a pilot of a small plane must begin a 6-degree descent starting from a height of 1150 feet above the ground. To the nearest tenth of a foot, how many feet from the runway is the airplane at the start of this approach (ground distance)?

a) 11.5 feet
b) 115 feet
c) 204.2 feet
d) 1040.2 feet

Answer 1

To calculate the ground distance from the runway, use the tangent function and the given height and descent angle. The plane is approximately 1040.2 feet from the runway at the start of the approach.

Step-by-step explanation:

To calculate the ground distance from the runway, we need to find the horizontal distance traveled by the plane during the descent. We can use trigonometry to find this distance.

Given that the plane begins the descent at a height of 1150 feet and the descent angle is 6 degrees, we can use the tangent function to calculate the horizontal distance (ground distance) traveled by the plane.

Tangent of the descent angle = Opposite/Adjacent. In this case, the Opposite is the height of the plane (1150 feet) and the Adjacent is the ground distance we want to find.

Tan(6 degrees) = 1150/Adjacent.

From this equation, we can solve for Adjacent:

Adjacent = 1150/Tan(6 degrees) ≈ 1040.2 feet.

Therefore, the plane is approximately 1040.2 feet from the runway at the start of the approach.