Law of Sines and Law of Cosines — a Deeper Look — Quiz

Question 8 • Precalculus

Sophia wants to solve for the side length of b Which equation could Sophia use to solve for the side length of b , given the other two side lengths and the measure of their included angle?

Answer

b squared is equal to A squared plus c squared minus 2 A b cosine cap c

b squared is equal to A squared plus c squared minus 2 A c cosine cap A

b squared is equal to A squared plus c squared minus 2 A c cosine cap c

b squared is equal to A squared plus c squared minus 2 A c cosine cap b

Explanation

The Law of Cosines says that the square of a side equals the sum of the squares of the other two sides minus twice their product times the cosine of the included angle. For side b, the other sides are a and c, and the included angle is B, so the equation is b² = a² + c² − 2ac cos(B). That matches choice D.

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