Answer
$B \approx 67.22^{\circ}$, $C \approx 82.78^{\circ}$ and $a \approx 5.04$
Work Step by Step
Use Law of Cosines to find $a$: $a=\sqrt {b^2+c^2-2bc \cos A}=\sqrt{(8)^2+(10)^2-(2)(8) \cos 30^{\circ}} \approx 5.04$
Use Law of Cosines to find $B$: $\dfrac{a}{\sin A}=\dfrac{C}{\sin A}$
This implies that $\sin C=\dfrac{10 \sin 30^{\circ}}{5.04} \implies C \approx 82.78^{\circ}$
and $B=180^{\circ}-30^{\circ}-82.78^{\circ}=67.22^{\circ}$
Our answers are: $B \approx 67.22^{\circ}$, $C \approx 82.78^{\circ}$ and $a \approx 5.04$.
