Finding Side Length in a Triangle Using Law of Sines

In triangle ABC, the lengths of the sides are given as follows: side AB measures 12 cm, side AC measures 16 cm, and side BC is represented as $x$ cm. Triangle ABC is inscribed in a circle of radius 10 cm. In addition, the angle opposite side BC, angle A, is given a measure of 60 degrees. What is the length of side BC, $x$?

To solve for $x$, you can utilize the Law of Sines, which states that for any triangle, the ratios of the lengths of the sides to the sines of their corresponding opposite angles are equal:

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

Here, you will need to find angle B or angle C to determine the lengths of the sides.