Chapter 12.5, Problem 6P

To determine

Find the distance (measured along the ground) from the airport at which the pilot must start the descent.

Answer to Problem 6P

About 48900 meters.

Explanation of Solution

Given:

The approach pattern to an airport requires pilots to set an $11°$ angle of descent toward the runway.A plane is flying at an altitude of 9500 m.

Formula Used:

  $\tan \theta =\frac{\text{length of opposite side to }\theta }{\text{length of adjacent side to }\theta }$

Calculation:

Represent the given situation :

  

We need to find x .

Use the tan formula :

  $\begin{array}{l}\tan 11°=\frac{\text{length of opposite side to 11}°}{\text{length of adjacent side to 11}°}\\ \Rightarrow \tan 11°=\frac{9500}{x}\\ \Rightarrow x=\frac{9500}{\tan 11°}\mathrm{.................}[\text{multiply each side by }\frac{x}{\tan 11°}]\\ \Rightarrow x\approx 48900\end{array}$

So, the distance (measured along the ground) from the airport at which the pilot must start the descent is about 48900 meters.