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Question 8 • Mathematics III

On which triangle can the law of cosines be used to find the length of an unknown side? Law of cosines: A squared is equal to b squared plus c squared minus 2 b c cosine cap A

Answer

Image with description Triangle Q R S is shown. The measure of the angle R S Q is 57 degrees. The length of the sides R S, S Q, and Q R are labeled as 7, 12, and s.

Image with description Triangle Q R S is shown. The measure of the angles Q R S, R S Q, and S Q R are 87, 57, and 36 degrees. The length of the sides R S, S Q, and Q R are labeled as q, 12, and s.

Image with description Triangle Q R S is shown. The measure of the angles R S Q and R Q S are 57 and 36 degrees. The length of the sides R S, S Q, and Q R are labeled as q, 12, and s.

Image with description Triangle Q R S is shown. The measure of the angles R S Q and R Q S are 57 and 36 degrees. The length of the sides R S, S Q, and Q R are labeled as 7, b, and s.

Explanation

The law of cosines finds an unknown side when you know two sides and the angle between them. In choice C, the sides are 7 and 12, and the 57° angle is between those sides, so the law of cosines can find the third side, s. The other choices do not give two known sides with the included angle.

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