Answer
The value of $B$ is $31.5\text{ }\!\!{}^\circ\!\!\text{ }$.
Work Step by Step
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.
$B=31.5\text{ }\!\!{}^\circ\!\!\text{ }$
