I need some help on the following question:
In the triangle ABC to calculate the lengths of sides AB and BC.
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.