Chapter 12.5, Problem 2P

To determine

Find the angle of elevation of the kite.

Answer to Problem 2P

  $53.1°$

Explanation of Solution

Given:

A boy flying a kite is standing 30 ft from a point directly under the kite.The string to the kite is 50 ft long.

Formula Used:

  $\cos \theta =\frac{\text{length of adjacent side to }\theta }{\text{length of hypotenuse}}$

Calculation:

Represent the given situation :

  

We need to find x .

Use the cosine formula :

  $\begin{array}{l}\cos x=\frac{\text{length of adjacent side to }x}{\text{length of hypotenuse}}\\ \Rightarrow \cos x=\frac{30}{50}\\ \Rightarrow x={\cos }^{-1}\left(\frac{30}{50}\right)\mathrm{.............}[take{\text{ cos}}^{-1}\text{ each side]}\\ \Rightarrow x=53.1°\end{array}$

So, the angle of elevation of the kite is $53.1°$ .