Added some labels.....

So, obviously side "b" is easy enough, 8.544.

And I know that

sin(B) / b = sin(A) /a = sin(C) / c

So for the B/b angle/side:

0.866 / 8.544 = 0.101

But, I'm totally stumped at what to do next.

I could make it into some right angled triangles:

But not sure how that helps me, as neither triagle has enough information to use the basic SOH-CAH-TOA rules.

Hope someone can give me some pointers, thanks