Question

an airplane pilot wishes to make his approach to an airstrip at an angle of 23° with the horizontal. if he is flying at an altitude of 6200 feet, approximately how far from the airstrip should he begin his descent?

Explanation:

Step1: Use trigonometric ratio

We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 23^{\circ}\), the opposite side (altitude) \(y = 6200\) feet, and we need to find the adjacent side \(x\) (distance from the airstrip). So, \(\tan(23^{\circ})=\frac{6200}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to \(x=\frac{6200}{\tan(23^{\circ})}\). Since \(\tan(23^{\circ})\approx0.4245\), then \(x=\frac{6200}{0.4245}\approx14606\) feet.

Answer:

14606 feet