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AssignmentMultiple Choice

Law of Cosines

Question 1 • Fall 24 GMS Geometry: Concepts and Connections B

Which equation correctly uses the law of cosines to solve for the length s?

Answer
A
92 = s2 + 102 – 2(s)(10)cos(100°)
B
9 = s + 10 – 2(s)(10)cos(100°)
C
102 = s2 + 100 – 2(s)(10)cos(100°)
D
s2 = 92 + 102 – 2(9)(10)cos(100°)

Explanation

The law of cosines is c² = a² + b² − 2ab cos(C), where C is the included angle. Here the sides around the 100° angle are 9 and 10, and the opposite side is s, so s² = 9² + 10² − 2(9)(10)cos(100°). That matches choice D.

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