Chapter 13, Problem 1E

To determine

To calculate: The angle of elevation of the plane during the takeoff.

Answer to Problem 1E

(C) $19.6°$

Explanation of Solution

Given information:Afetr travelling 800 yards horizontallty, the plane has climbed 285 yards vertically.

Formula used: Let the horizontal distance traveled by plane is $BC$ , and the distance traveled vertically is $CD$ . If, $x$ is the angle of elevation of the given triangle, then $\tan (x)=\frac{CD}{CB}$

  

Calculation:Plugging the values in $\tan (x)=\frac{CD}{CB}$ we get,

  

  $\begin{array}{l}\tan (x)=\frac{CD}{CB}\\ \tan (x)=\left(\frac{285}{800}\right)\end{array}$

Now, taking arctan both sides we get,

  $\begin{array}{l}{\tan }^{-1}(\tan (x))={\tan }^{-1}\left(\frac{285}{800}\right)\\ x={\tan }^{-1}\left(\frac{285}{800}\right)\\ x={\tan }^{-1}(0.357)\\ x=19.64°\end{array}$

So, the angle of elevation of the plane is $19.6°$