We use the cosine rule:
AC^2=AB^2+BC^2-2AB•BCcosB=36+27.04-2*6*5.2cos150=117.08 approx.
AC=√117.08=10.82cm approx.
Now we use the sine rule: sinA/BC=sinB/AC=sinC/AB. We need angle C and we have angle B and sides AB and AC, so sin150/10.82=sinC/6; sinC=6sin150/10.82=0.2773 approx. C=16.10 degrees approx. (sin150=0.5, cos150=-√3/2=-0.8660 approx).