1. **State the problem:** We have a right triangle with one leg of length 7, an angle of 45° opposite side $a$, and hypotenuse $b$. We need to find the length of side $b$. 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. **Identify the sides:** Since the angle opposite $a$ is 45°, and the right angle is at the bottom-left, the triangle is isosceles right triangle with legs $a$ and 7. 4. **Since the legs are equal in a 45°-45°-90° triangle,** we have $a = 7$. 5. **Calculate the hypotenuse $b$ using the formula:** $$b = a \times \sqrt{2}$$ 6. **Substitute $a = 7$:** $$b = 7 \times \sqrt{2}$$ 7. **Final answer:** $$b = 7\sqrt{2}$$ This means the hypotenuse $b$ is $7\sqrt{2}$ units long.