Chapter 6, Problem 76RE

To determine

Find the side labelled $x$ .

Answer to Problem 76RE

  $B=153.15$

Explanation of Solution

Given information:

Formula used:

  $\begin{array}{l}\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}\\ \\ A+B+C={180}^{°}\end{array}$

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

  $\begin{array}{l}\frac{\sin A}{a}=\frac{\sin C}{c}\\ \\ \frac{\sin A}{5}=\frac{\sin {10}^{°}}{3}\\ \\ \sin A=\frac{5\left(\sin {10}^{°}\right)}{3}\\ \\ \sin A=0.29\end{array}$

  $A={16.85}^{°}$

By using angle sum property $A+B+C={180}^{°}$ :

  $\begin{array}{l}A+B+C={180}^{°}\\ \\ {16.85}^{°}+B+{10}^{°}={180}^{°}\\ \\ B={180}^{°}-{26.85}^{°}\\ \\ \boxed{B=153.15}\end{array}$