Non-Right Triangle Trigonometry

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

Use when: angle-side pair + one more piece.

$c^2 = a^2 + b^2 - 2ab\cos C$ (finding a side)

$\cos C = \frac{a^2 + b^2 - c^2}{2ab}$ (finding an angle)

Use when: SAS or SSS.

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

SSA can give 0, 1, or 2 triangles. Check if the angle found could be obtuse.

$a = 8$, $b = 11$, $C = 40°$. $c^2 = 64 + 121 - 176\cos 40° = 185 - 134.8 = 50.2$. $c \approx 7.09$.

Area = $\frac{1}{2}(8)(11)\sin 40° \approx 28.3$.