Question

an airplane pilot wishes to make his approach to an airstrip at an angle of 10° with the horizontal. if he is flying at an altitude of 5000 feet, approximately how far from the airstrip should he begin his descent? (give answer to the nearest 100 feet).

Explanation:

Step1: Use the tangent function

We know that in a right - triangle (where the altitude is the opposite side and the horizontal distance from the airstrip is the adjacent side with respect to the given angle), the tangent of an angle $\theta$ is defined as $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 10^{\circ}$ and the opposite side $y = 5000$ feet. Let the adjacent side (horizontal distance) be $x$. So, $\tan(10^{\circ})=\frac{5000}{x}$.

Step2: Solve for $x$

We can rewrite the equation from Step1 as $x=\frac{5000}{\tan(10^{\circ})}$. Since $\tan(10^{\circ})\approx0.1763$, then $x=\frac{5000}{0.1763}\approx28361$. Rounding to the nearest 100 feet, $x\approx28400$.

Answer:

28400 feet