Finding Length of Side BC in Triangle ABC with Given Angles

In triangle ABC, the lengths of sides AB and AC are 12 and 16, respectively. The angle opposite side BC is denoted as angle A. If angle A is twice the measure of angle B, what is the length of side BC?

Use the Law of Sines, which states that:

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

where $a$, $b$, and $c$ are the lengths of sides opposite angles A, B, and C respectively.