The cosine rule: a^2 = b^2 + c^2 - 2bc cosA (and cyclic permutations). Rearranged: cosA = (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.