If you have a triangle ABC where AB=8, BC=4, and D is a point on AC where BD is a straight line that bisects angle B, and angle B is 120 degrees, what is the length of BD?

I tried using cosine law where AC=sqrt(88), angle C = arcsin(8sin(120 degrees)/sqrt(88)), angle BDC = 120-angle C and BD was thus (4*angle C)/(120-angle BDC), but I think I messed up somewhere?