## Trigonometry (11th Edition) Clone

$B=41.7^{\circ}$
The law of sines in the case of this question is: $\frac{b}{\sin B}=\frac{c}{\sin C}$ We substitute the values of $b,c$ and $C$ in the formula to find $B$: $\frac{b}{\sin B}=\frac{c}{\sin C}$ $\frac{58.2}{\sin B}=\frac{68.3}{\sin 51.3}$ $\sin B\times68.3=58.2\times \sin 51.3$ $\sin B=\frac{58.2\times \sin 51.3}{68.3}$ We use a calculator to find the value of $\sin 51.3$: $\sin B=\frac{58.2\times \sin 51.3}{68.3}$ $\sin B=\frac{58.2\times 0.78043}{68.3}$ $\sin B=0.66502$ $B=\sin^{-1} 0.66502$ $B=41.68\approx41.7$ Therefore, $B=41.7^{\circ}$.