Chapter 12, Problem 17CR

To determine

Find the angle that wires make with each other.

Answer to Problem 17CR

A

Explanation of Solution

Given:

Wires of lengths 20 m and 30 m extend from the top of a tower to the ground on the same side of the tower.The shorter wire makes an angle of $42°$ with the ground.

Calculation:

Represent the situation and solve :

  

In the smaller triangle:

  $\begin{array}{l}\sin 42°=\frac{\text{length of the side opposite to }42°}{\text{length of hypotenuse}}\\ \Rightarrow \sin 42°=\frac{h}{20}\\ \Rightarrow h=20\sin 42°\\ \Rightarrow h\approx 13.383\end{array}$

In the bigger triangle,

  $\begin{array}{l}\cos \theta =\frac{\text{length of the side adjacent to }\theta }{\text{length of hypotenuse}}\\ \Rightarrow \cos \theta =\frac{13.383}{30}\\ \Rightarrow \theta ={\cos }^{-1}(0.4461)\\ \Rightarrow \theta \approx 63.5°\end{array}$

So, the angle between the wires is $63.5°-48°=15.5°$

So, the correct option is A.