Finding Side Length in Triangle Using Law of Sines

In triangle ABC, angle A measures 30 degrees, angle B measures 45 degrees, and the length of side c (opposite to angle C) is 10 units. Using the Law of Sines to find the lengths of sides a (opposite to angle A) and b (opposite to angle B), determine the value of $b$.

Recall that the Law of Sines states that:

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

Use these properties to solve for side $b$.