## Precalculus (6th Edition) Blitzer

The value of $B$ is $31.5\text{ }\!\!{}^\circ\!\!\text{ }$.
On solving the provided expression for B: \begin{align} & \frac{81}{\sin 43\text{ }\!\!{}^\circ\!\!\text{ }}=\frac{62}{\sin B} \\ & \sin B=\frac{62\times \sin 43\text{ }\!\!{}^\circ\!\!\text{ }}{81} \end{align} $\sin 46\text{ }\!\!{}^\circ\!\!\text{ }=0.68199836$ Use this value in the above expression to get \begin{align} & \sin B=\frac{62\times 0.68199836}{81} \\ & =\frac{42.283898}{81} \\ & =0.52202 \end{align} Then, take sine on the right side and find the value. $B={{\sin }^{-1}}\left( 0.52202 \right)$ ${{\sin }^{-1}}\left( 0.52202 \right)=31.46807$ Round off to the nearest decimal. $B=31.5\text{ }\!\!{}^\circ\!\!\text{ }$