To find side AB of triangle ABC given points M, N, and C, the initial assumption of triangle similarity is incorrect, complicating the solution. The sine rule is applied in triangles BNC and BMA, yielding four equations to solve for the unknowns. After eliminating variables, the relation between angles leads to the conclusion that side AB measures 22.5. An alternative approach using coordinate geometry simplifies the problem by establishing a right triangle relationship. The discussion highlights the complexity of the problem while offering different methods to reach the solution.