Answer
$B \approx26.39^{\circ}$, $c \approx 15^{\circ}$ and $C=123.61^{\circ}$
Work Step by Step
Use law of sines to find angle $B$: $\dfrac{a}{\sin A}=\dfrac{b}{\sin B}$
This implies that $\sin B=\dfrac{8 \sin 30^{\circ}}{9} \implies B \approx 26.39^{\circ}$
and $C=180^{\circ}-30^{\circ}-26.39^{\circ}=123.61^{\circ}$
Use law of sines to find $c$: $\dfrac{a}{\sin A}=\dfrac{c}{\sin C}$
This implies that $c=\dfrac{9 \sin 123.61^{\circ}}{\sin 30^{\circ}} \implies c \approx 15^{\circ}$
Our answers are: $B \approx26.39^{\circ}$, $c \approx 15^{\circ}$ and $C=123.61^{\circ}$
