1. **State the problem:** We have a right triangle with one leg measuring 12 centimeters, the hypotenuse measuring 19 centimeters, and the other leg unknown. We need to find the missing side length. 2. **Formula used:** The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse ($c$) equals the sum of the squares of the legs ($a$ and $b$): $$c^2 = a^2 + b^2$$ 3. **Identify known values:** Here, $c = 19$ cm (hypotenuse), $a = 12$ cm (one leg), and $b$ is unknown. 4. **Set up the equation:** $$19^2 = 12^2 + b^2$$ 5. **Calculate squares:** $$361 = 144 + b^2$$ 6. **Isolate $b^2$:** $$b^2 = 361 - 144$$ $$b^2 = 217$$ 7. **Find $b$ by taking the square root:** $$b = \sqrt{217}$$ 8. **Estimate with a calculator:** $$b \approx 14.7$$ centimeters (rounded to one decimal place). **Final answer:** The missing side length is approximately **14.7 centimeters**.