1. **Problem statement:** We have a right triangle with angles 45°, 45°, and 90°. One leg length is 4, the hypotenuse length is $\sqrt{32}$, and the other leg length is $s$. We need to find $s$. 2. **Formula and rules:** In a 45°-45°-90° triangle, the legs are congruent, and the hypotenuse is $\sqrt{2}$ times the length of each leg. 3. **Using the property:** Let each leg be $x$. Then the hypotenuse is $x\sqrt{2}$. 4. **Given:** One leg is 4, so $x=4$. 5. **Calculate hypotenuse:** Hypotenuse should be $4\sqrt{2}$. 6. **Check given hypotenuse:** Given hypotenuse is $\sqrt{32}$. Simplify $\sqrt{32}$: $$\sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}$$ 7. **Conclusion:** The given hypotenuse matches the expected value for leg length 4. 8. **Find $s$:** Since legs are equal in a 45°-45°-90° triangle, $s = 4$. **Final answer:** $s = 4$ (Option A).