Question

To approach Runway 17 of the Ponca City Municipal Airport in Oklahoma, the pilot must begin a 3⁰

descent starting from an altitude of 2714 feet above sea level. The airport has an altitude of 1007 feet above sea
level. How far must the airplane fly during its descent? (Find both the ground distance and actual distance

Answer 1

To solve this problem, we can use trigonometry and the Pythagorean theorem.

First, we need to calculate the height that the plane needs to descend. We can do this by multiplying the horizontal distance by the tangent of the descent angle:

tan(3⁰) = 0.0524

2714 - 1007 = 1707 feet

Therefore, the height the plane needs to descend is:

0.0524 x 1707 = 89.36 feet

Next, we can calculate the ground distance using the Pythagorean theorem:

d^2 = 89.36^2 + x^2

where d is the ground distance and x is the horizontal distance.

We know that the altitude of the airport is 1007 feet, so the total altitude change is:

2714 - 1007 = 1707 feet

We can use this information to solve for x:

x^2 = 1707^2 - 89.36^2

x = 1706.58 feet

Therefore, the ground distance the plane must fly during its descent is approximately 1706.58 feet, and the actual distance is approximately 1707.36 feet.