Answer
$C= 50^\circ$
$a \approx11.82$
$c\approx9.19$
Work Step by Step
Step 1. Using the given figure and conditions, we have $C=180-100-30=50^\circ$
Step 2. Using the Law of Sines, we have $\frac{a}{sin100^\circ}=\frac{c}{sin50^\circ}=\frac{6}{sin30^\circ}$
Step 3. Thus $a=\frac{6sin100^\circ}{sin30^\circ} \approx11.82$ and $c=\frac{6sin50^\circ}{sin30^\circ}\approx9.19$
