I think you must have a typo in your problem. If AB=x and AC=2x, then from the law of sines you have:

which is impossible. I wonder if the problem statement should have said: "Side AB is twice that of BC?" If so, then let length BC = x, AB=2x, and AC = y, and from the law of sines you have:

and from law of cosines:

Sub this back into the previous equation and solve for