1. **State the problem:** The cosine rule (or law of cosines) relates the lengths of sides of a triangle to the cosine of one of its angles. It states: $$c^2 = a^2 + b^2 - 2ab\cos C$$ where $a$, $b$, and $c$ are sides of the triangle and $C$ is the angle opposite side $c$. 2. **Use case:** Given two sides $a$ and $b$, and the included angle $C$, find side $c$. 3. **Example:** Suppose $a=5$, $b=7$, and angle $C=60^\circ$. 4. **Calculate $c^2$:** $$c^2 = 5^2 + 7^2 - 2\times 5 \times 7 \times \cos 60^\circ = 25 + 49 - 70 \times 0.5 = 74 - 35 = 39$$ 5. **Calculate $c$:** $$c = \sqrt{39} \approx 6.245$$ 6. **Explanation:** We use the cosine rule to find an unknown side given two known sides and the included angle by substituting values into the formula and simplifying step-by-step. Thus, using the cosine rule, side $c$ is approximately $6.245$.