Finding Side Length in a Triangle Using Law of Sines

Consider triangle ABC with angle A measuring 30 degrees and the side lengths being represented as follows: side a (opposite angle A) is equal to $x$, side b (opposite angle B) is equal to $4$, and side c (opposite angle C) is the length we need to find. Using the Law of Sines, we can establish the following relationship:

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

Given that angle B is 60 degrees, we need to determine the length of side c. First, find the sine of angle A and angle B, and then use the information to find side c in terms of x.