Exercises: Prove the Laws of Sines and Cosines

Complete the key step in the Law of Sines proof. In triangle $ABC$, altitude $h$ from $C$ gives $h = b \sin A$ and $h = a \sin B$. Setting them equal: $b \sin A = a \sin B$. After dividing both sides by $\sin A \cdot \sin B$, the result is:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲