1. **Problem Statement:** We need to find the length of the hypotenuse $c$ in a right triangle where the legs are $a=10$ and $b=11$. 2. **Formula:** The Pythagorean Theorem states that for a right triangle: $$c^2 = a^2 + b^2$$ This means the square of the hypotenuse equals the sum of the squares of the other two sides. 3. **Substitute the known values:** $$c^2 = 10^2 + 11^2$$ 4. **Calculate the squares:** $$c^2 = 100 + 121$$ 5. **Add the values:** $$c^2 = 221$$ 6. **Find $c$ by taking the square root:** $$c = \sqrt{221}$$ 7. **Simplify the square root if possible:** 221 factors as $13 \times 17$, which are primes, so it cannot be simplified further. 8. **Final answer:** $$c = \sqrt{221} \approx 14.87$$ So, the missing length $c$ is approximately 14.87 units.