Finding Side Length Using Law of Sines

A triangle has an angle A that measures $30^{ ext{o}}$. The length of the side opposite to angle A is 10 units. Using the Law of Sines, find the length of the side opposite to angle B, which measures $45^{ ext{o}}$. Express your answer as a decimal, rounded to two decimal places.

Recall that the Law of Sines states:

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

where:

• $a$ is the length of the side opposite to angle A
• $b$ is the length of the side opposite to angle B
• $A$ and $B$ are the measures of angles A and B, respectively