How do you determine the angle of a triangle given sides a, b, c using the Law of Cosines?

How do you determine the angle of a triangle given sides a, b, c using the Law of Cosines?

• A. cos(C) = (a^2 + b^2 - c^2)/(2ab)
• B. cos(C) = (a^2 + c^2 - b^2)/(2ac)
• C. cos(C) = (b^2 + c^2 - a^2)/(2bc)
• D. c^2 = a^2 + b^2 + 2ab cos(C)

Answer: (A)

When you use the Law of Cosines, you relate a side to the other two sides and the cosine of the included angle. For angle C, which lies between sides a and b and is opposite side c, the law says c^2 = a^2 + b^2 - 2ab cos(C). Solving for cos(C) gives cos(C) = (a^2 + b^2 - c^2) / (2ab). This is the expression that yields the angle C from the three side lengths. The other forms would correspond to different angles (using the appropriate adjacent sides) or would use the wrong sign in front of the 2ab cos(C).

When you use the Law of Cosines, you relate a side to the other two sides and the cosine of the included angle. For angle C, which lies between sides a and b and is opposite side c, the law says c^2 = a^2 + b^2 - 2ab cos(C). Solving for cos(C) gives cos(C) = (a^2 + b^2 - c^2) / (2ab). This is the expression that yields the angle C from the three side lengths. The other forms would correspond to different angles (using the appropriate adjacent sides) or would use the wrong sign in front of the 2ab cos(C).