Chapter 12.5, Problem 3P

To determine

Find the angle that the cable makes with the ground.

Answer to Problem 3P

  $64.1°$

Explanation of Solution

Given:

A cable 4 m long is attached to a pole.The cable is staked to the ground 1.75 m from the base of the pole.

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 :

  $\begin{array}{l}\cos x=\frac{\text{length of adjacent side to }x}{\text{length of hypotenuse}}\\ \Rightarrow \cos x=\frac{1.75}{4}\\ \Rightarrow x={\cos }^{-1}\left(\frac{1.75}{4}\right)\mathrm{.............}[take{\text{ cos}}^{-1}\text{ each side]}\\ \Rightarrow x=64.1°\end{array}$

So, the angle that the cable makes with the ground is $64.1°$ .