1. **State the problem:** A hockey player is aiming at a goalie net with posts 2.0 m apart. The player is 7.0 m from one post and 8.2 m from the other post. We need to find the angle within which the player must shoot the puck to get it in the net. 2. **Identify the triangle and angle:** The player and the two posts form a triangle with sides 7.0 m, 8.2 m, and 2.0 m. We want to find the angle at the player's position between the two posts. 3. **Use the Law of Cosines:** For a triangle with sides $a$, $b$, and $c$, and angle $\theta$ opposite side $c$, the law states: $$\cos(\theta) = \frac{a^2 + b^2 - c^2}{2ab}$$ Here, $a=7.0$, $b=8.2$, and $c=2.0$ (distance between posts). 4. **Calculate $\cos(\theta)$:** $$\cos(\theta) = \frac{7.0^2 + 8.2^2 - 2.0^2}{2 \times 7.0 \times 8.2} = \frac{49 + 67.24 - 4}{114.8} = \frac{112.24}{114.8}$$ 5. **Simplify fraction:** $$\cos(\theta) = \frac{\cancel{112.24}}{\cancel{114.8}} \approx 0.9779$$ 6. **Find angle $\theta$:** $$\theta = \arccos(0.9779) \approx 12.0^\circ$$ 7. **Interpretation:** The player must shoot within an angle of approximately $12.0^\circ$ to get the puck between the posts. **Final answer:** The shooting angle is about $12.0^\circ$.