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,
$$
\begin{aligned}
\text{Area} & = \frac{1}{2} bc \sin A \\
& = \frac{1}{2} ab \sin C \\
& = \frac{1}{2} ac \sin B
\end{aligned}
$$

E 5.6 Exercises