Area of Triangle with Given Angles and Side Length

In triangle ABC, the lengths of the sides are given as follows: side AB measures 12 units, angle A measures 45 degrees, and angle B measures 60 degrees. Determine the area of triangle ABC.

Recall that the area of a triangle can be calculated using the formula: $$ ext{Area} =\frac{1}{2}ab ext{sin}(C)$$, where $a$ and $b$ are the lengths of two sides, and $C$ is the angle between these two sides.