1. **Stating the problem:** We have a right triangle with one angle of 45°. The side opposite the 45° angle is $3\sqrt{2}$, the hypotenuse is $x$, and the base is $y$. 2. **Recall the properties of a 45°-45°-90° triangle:** In such a triangle, the legs are equal, and the hypotenuse is $\sqrt{2}$ times the length of each leg. 3. **Given the side opposite 45° is $3\sqrt{2}$, this is one leg.** Since the legs are equal, the other leg $y$ is also $3\sqrt{2}$. 4. **Find the hypotenuse $x$ using the formula:** $$x = \text{leg} \times \sqrt{2}$$ Substitute the leg value: $$x = 3\sqrt{2} \times \sqrt{2}$$ 5. **Simplify the expression:** $$x = 3 \times \cancel{\sqrt{2}} \times \cancel{\sqrt{2}} = 3 \times 2 = 6$$ 6. **Final answers:** $$x = 6$$ $$y = 3\sqrt{2}$$