I note that in equation (II) you have x instead of sin(x).
You don’t need the Sine Rule in a right triangle. So, for example, m=bsin(x) by definition of sine, and m=acos(x-24), which means that bsin(x)=acos(x-24). You have the right idea.
When you find x, check your answer by computing the lengths of the sides of the square after working out all the angles, and make sure that the sides are in fact equal.