Consider Sin 27 and Tan 27 and relate them to the length that is given. If you need more help please don't hesitate to reply me.
The way you did is incorrect. I assume that you tried to use the Sine rule. But you have applied it incorrectly. In the first line you have written it should be 15/Sin27=BC/Sin90. But as "Prove It" had shown it could be done easily if you consider the Trignometric ratios of right traingles.