Answer
$a\approx2.05$
$B\approx47.0^\circ$
$C\approx103.0^\circ$
Work Step by Step
1. Use the Law of Cosines, we have $a^2=(3)^2+(4)^2-2(3)(4)cos30^\circ\approx4.2154$, thus $a\approx2.05$
2. Use the Law of Sines, we have $\frac{sinB}{3}=\frac{sinC}{4}=\frac{sin30^\circ}{2.05}$
3. We have $B=sin^{-1}(\frac{3sin30^\circ}{2.05})\approx47.0^\circ$
4. We have $C\approx180-30-47.0=103.0^\circ$
