The Law of Cosines, given sides a, b and included angle C, gives the third side c as:
A$c = a + b - 2ab \cos C$ (linear sum form)
B$c^2 = a^2 + b^2 + 2ab \cos C$ (wrong sign)
C$c^2 = a^2 + b^2 - 2ab \cos C$ (the correct form)
D$c^2 = a^2 + b^2$ (Pythagoras only valid for C=90°)
Answer & Solution
Correct answer: C. $c^2 = a^2 + b^2 - 2ab \cos C$ (the correct form)
Law of Cosines: c² = a² + b² − 2ab cos C. For C = 90°, cos 90° = 0 → reduces to Pythagoras. Useful for SAS (2 sides + included angle) and SSS (all 3 sides given) cases.
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