Which equation represents the Law of Cosines for a triangle with sides a, b, and c opposite angles A, B, and C respectively?

Which equation represents the Law of Cosines for a triangle with sides a, b, and c opposite angles A, B, and C respectively?

• A. c² = a² + b² - 2ab cos C
• B. a² = b² + c² - 2bc cos A
• C. b² = a² + c² - 2ac cos B
• D. a² + b² = c² - 2ab cos C

Answer: (A)

The Law of Cosines says a side’s square equals the sum of the squares of the other two sides minus twice their product times the cosine of the angle between those two sides. The angle between sides a and b is angle C, since C is opposite side c. So the correct form for side c is c^2 = a^2 + b^2 − 2ab cos C. This directly ties the side c to the two adjacent sides a and b and the included angle C. (Equivalently, you could write analogous formulas for the other sides, such as a^2 = b^2 + c^2 − 2bc cos A and b^2 = a^2 + c^2 − 2ac cos B, but the form for c uses the included angle C between a and b.)

The Law of Cosines says a side’s square equals the sum of the squares of the other two sides minus twice their product times the cosine of the angle between those two sides. The angle between sides a and b is angle C, since C is opposite side c. So the correct form for side c is c^2 = a^2 + b^2 − 2ab cos C. This directly ties the side c to the two adjacent sides a and b and the included angle C.

(Equivalently, you could write analogous formulas for the other sides, such as a^2 = b^2 + c^2 − 2bc cos A and b^2 = a^2 + c^2 − 2ac cos B, but the form for c uses the included angle C between a and b.)