Sine and Cosine Rules

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

Use when you have a side-angle pair and one other measurement.

Finding a Side

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

Finding an Angle

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

Finding a Side

$a^2 = b^2 + c^2 - 2bc\cos A$

Use when you know two sides and the included angle (SAS).

Finding an Angle

$\cos A = \frac{b^2 + c^2 - a^2}{2bc}$

Use when you know three sides (SSS).

$\text{Area} = \frac{1}{2}ab\sin C$

Use when you know two sides and the included angle.