1. **Problem statement:** Draw a triangle and explain the Law of Cosines. 2. **Law of Cosines formula:** For a triangle with sides $a$, $b$, and $c$, and angle $\gamma$ opposite side $c$, the law states: $$c^2 = a^2 + b^2 - 2ab\cos(\gamma)$$ 3. **Explanation:** This formula relates the lengths of the sides of a triangle to the cosine of one of its angles. It generalizes the Pythagorean theorem for any triangle, not just right triangles. 4. **Diagram description:** We draw triangle $ABC$ with sides $a = BC$, $b = AC$, and $c = AB$. Angle $\gamma$ is at vertex $C$ opposite side $c$. 5. **Use:** If you know two sides and the included angle, you can find the third side using the formula above. 6. **Example:** If $a=5$, $b=7$, and $\gamma=60^\circ$, then $$c^2 = 5^2 + 7^2 - 2 \times 5 \times 7 \times \cos(60^\circ) = 25 + 49 - 70 \times 0.5 = 74 - 35 = 39$$ $$c = \sqrt{39} \approx 6.24$$ This shows how to apply the law to find side $c$.