Area of Triangle Based on Angles

In triangle ABC, angle A measures $60^{\circ}$, angle B measures $70^{\circ}$, and the length of side a (opposite angle A) is 12 units. Calculate the area of triangle ABC.

To find the area of triangle ABC, you can use the formula:

Area = $\frac{1}{2}ab \sin(C)$

Where $a$ and $b$ are the lengths of two sides and $C$ is the angle between them. First, you need to find the lengths of sides b and c using the Law of Sines:

$$\frac{a}{\sin(A)} = \frac{b}{\sin(B)} = \frac{c}{\sin(C)}$$