Law of sines & cosines

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   In triangle $ABC$, $a = 12$, $b = 20$, and the included angle $C = 120^{\circ}$, so $\cos C = -\frac{1}{2}$. Use the law of cosines to find the third side $c$.

2. Warm-up

   In triangle $ABC$, $a = 9$, $b = 15$, and the included angle $C = 120^{\circ}$, so $\cos C = -\frac{1}{2}$. Use the law of cosines to find the third side $c$.

3. Warm-up

   In triangle $ABC$, $a = 18$, $b = 30$, and the included angle $C = 120^{\circ}$, so $\cos C = -\frac{1}{2}$. Use the law of cosines to find the third side $c$.

Problems shown under their original terms: Generated (template, solver-computed).