1. **Problem:** Find the missing side length $AC$ in a right triangle with sides $AB=12$ yd, hypotenuse $BC=15$ yd. 2. **Formula:** Use the Pythagorean theorem: $$a^2 + b^2 = c^2$$ where $c$ is the hypotenuse. 3. **Apply:** Here, $a=AB=12$, $c=BC=15$, and $b=AC$ unknown. 4. **Calculate:** $$AC^2 = BC^2 - AB^2 = 15^2 - 12^2 = 225 - 144 = 81$$ 5. **Simplify:** $$AC = \sqrt{81} = 9$$ 6. **Answer:** The missing length $AC$ is 9 yd. This completes the first problem.