Triangular Relations

Using the standard upper-lowercase relations between angles ($\alpha$,$\beta$,$\gamma$) and opposite sides (A,B,C), one has

$$A^2 = B^2 + C^2 - 2 B C \cos \alpha$$

and

$$\frac{\sin \alpha}{A} = \frac{\sin \beta}{B} = \frac{\sin \gamma}{C}$$