Answer
$B=100{}^\circ,b\approx 26.1$ and $c\approx 10.8$.
Work Step by Step
First we will find the value of B
Properties of a triangle:
Sum of three angles is $A+B+C=180{}^\circ $
$\begin{align}
& A+B+C=180{}^\circ \\
& 56{}^\circ +B+24{}^\circ =180{}^\circ \\
& B=180{}^\circ -80{}^\circ \\
& B=100{}^\circ
\end{align}$
Now, we will find the remaining sides using the ratio:
$\frac{a}{\sin A}$,or $\frac{22}{\sin 56{}^\circ }$,
Now, we will use the law of sines to find b.
$\begin{align}
& \frac{b}{\sin B}=\frac{a}{\sin A} \\
& \frac{b}{\sin 100{}^\circ }=\frac{22}{\sin 56{}^\circ } \\
& b=\frac{22\sin 100{}^\circ }{\sin 56{}^\circ } \\
& b\approx 26.1
\end{align}$
Using the law of sines again, we will find c.
$\begin{align}
& \frac{c}{\sin C}=\frac{a}{\sin A} \\
& \frac{c}{\sin 24{}^\circ }=\frac{22}{\sin 56{}^\circ } \\
& c=\frac{22\sin 24{}^\circ }{\sin 56{}^\circ } \\
& c\approx 10.8
\end{align}$
