How does one find the area of a generic triangle?

Despite probably being brought up using the A=1/2bh formula, there is a more generic formula that works for any triangle shape without any calculations needed to find the height perpendicular to a triangle's base. A=1/2a.b.sinC where C is the internal angle of the vertex opposite side c. If you think about why this is, it may strike you that we are in fact incorporating the sinC element to find the vertical height of the triangle, but we no longer need to analyze the angles etc for a non-uniform shape.