1. **State the problem:** We need to solve for $b$ in a right triangle where one leg is 6, the other leg is $b$, and the hypotenuse is 11. 2. **Formula used:** The Pythagorean Theorem states that for a right triangle, $$a^2 + b^2 = c^2$$ where $a$ and $b$ are the legs and $c$ is the hypotenuse. 3. **Apply the formula:** Here, $a = 6$, $b = b$, and $c = 11$. Substitute these values: $$6^2 + b^2 = 11^2$$ 4. **Calculate squares:** $$36 + b^2 = 121$$ 5. **Isolate $b^2$:** $$b^2 = 121 - 36$$ $$b^2 = 85$$ 6. **Solve for $b$ by taking the square root:** $$b = \sqrt{85}$$ 7. **Final answer:** $$b = \sqrt{85}$$ which is approximately 9.22. This means the length of the leg $b$ is $\sqrt{85}$ units.