Area of Triangle in Terms of Two Sides and Angle/Proof 2

Proof

 * TriangleAreaTwoSidesAngle-2.png

By definition of sine:
 * $h = b \sin C$

From Area of Triangle in Terms of Side and Altitude:
 * $\map \Area {ABC} = \dfrac {a h} 2$

Substituting:
 * $\map \Area {ABC} = \dfrac {a b \sin C} 2$