Chapter 12.7, Problem 12P

To determine

To determinethe angle that longer wire make with the ground.

Answer to Problem 12P

The angle between longer wire and the ground is ${64.6}^{\circ }$

Explanation of Solution

Given information :

  

Here $\angle ADC={90}^{\circ }+{53}^{\circ }={143}^{\circ }$

According to law of sines,

In any triangle ABC,

  

  $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$

Hence,

  $\begin{array}{l}\frac{30}{\sin {143}^{\circ }}=\frac{10}{\sin \angle ACD}\\ \sin \angle ACD=0.2006\\ \angle ACD={\sin }^{-1}0.2006\\ \angle ACD={11.6}^{\circ }\end{array}$

  $\angle ACB={53}^{\circ }+{11.6}^{\circ }={64.6}^{\circ }$

Hence the angle between longer wire and the ground is ${64.6}^{\circ }$