# 5.6 | Law of Sines

Law of Sines: If $$ABC$$ is a triangle with sides $$a,b,$$ and $$c,$$ then
$$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$
or
$$\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$$
The area of any triangle is one-half the product of the lengths of two sides times the sine of their included angle. That is,
\begin{aligned} \text{Area} & = \frac{1}{2} bc \sin A \\ & = \frac{1}{2} ab \sin C \\ & = \frac{1}{2} ac \sin B \end{aligned}