1. **State the problem:** We have a right triangle with one angle of 45°, the side adjacent to this angle is 10, the side opposite is $x$, and the hypotenuse is $y$. We need to find $x$ and $y$ in simplest radical form. 2. **Recall the properties of a 45°-45°-90° triangle:** In such a triangle, the legs are congruent, and the hypotenuse is $\sqrt{2}$ times the length of each leg. 3. **Identify the sides:** Since the angle is 45°, the side adjacent (10) and the side opposite ($x$) are legs of the triangle, so $x = 10$. 4. **Find the hypotenuse $y$ using the formula:** $$y = \text{leg} \times \sqrt{2}$$ Substitute the leg length: $$y = 10 \times \sqrt{2}$$ 5. **Final answers:** $$x = 10$$ $$y = 10\sqrt{2}$$ These are the values of $x$ and $y$ in simplest radical form.