The cosine rule: $a^2$ = $b^2$ + $c^2$ - 2bc cosA (and cyclic permutations). Rearranged: cosA = $\frac{b^2+c^2-a^2}{(2bc)}$. Use when given SAS (two sides and included angle) to find the third side, or SSS (three sides) to find any angle. The cosine rule generalizes the Pythagorean theorem — when A = 90 degrees, it reduces to $a^2$ = $b^2$ + $c^2$. The sign of cosA determines the angle type: positive means acute, zero means right, negative means obtuse. This is useful for classifying a triangle as acute, right, or obtuse given its three sides: if $a^2$ < $b^2$ + $c^2$ for the largest side a, the triangle is acute.