Question

On which triangle can the law of cosines be used to find the length of an unknown side?

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Triangle Q R S is shown. The length of Q R is s, the length of R S is q, and the length of Q S is 12. Angle R Q S is 36 degrees, angle Q S R is 57 degrees, and angle S R Q is 87 degrees.
Triangle Q R S is shown. The length of Q R is s, the length of R S is 7, and the length of Q S is 12. Angle R S Q is 57 degrees.
Triangle Q R S is shown. The length of Q R is s, the length of R S is 7, and the length of Q S is b. Angle R S Q is 57 degrees and angle S Q R is 36 degrees.
Triangle Q R S is shown. The length of Q R is s, the length of R S is q, and the length of Q S is 12. Angle R Q S is 36 degrees and angle Q S R is 57 degrees.

Answer 1

(b) Triangle QRS is shown. The length of QR is s, the length of RS is 7, and the length of QS is 12. Angle RSQ is 57 degrees.

Explanation:

The Law of Cosines can be used to find an unknown side when that side is opposite a known angle, and the lengths of the sides of that angle are known. That will be the case when the known sides share a vertex, and the angle at that vertex is known.