Answer
We need both laws to resolve the triangle.
Work Step by Step
By the law of cosine ($c^2=a^2+b^2-2ab\cdot \cos{(C)}$) we can count the third side. Then by the Law of Sines ($\frac{{\sin {A}}}{a} = \frac{{\sin {B}}}{b} = \frac{{\sin {C}}}{c})$) we can compute the rest two angles. We need both laws to resolve the triangle.
