Exercises: Derive the Formula A = (1/2)ab sin(C)

In the derivation of $A = \dfrac{1}{2}ab\sin(C)$, an altitude $h$ is drawn from vertex $B$ perpendicular to side $b$ (= $AC$). In the right triangle formed at vertex $C$, the sine definition gives $\sin(C) = \dfrac{h}{a}$. Solving for $h$: $h =$   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   . Substituting into $A = \dfrac{1}{2} \cdot b \cdot h$ gives $A =$   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .