1. **State the problem:** We need to find the length of side $XY$ in a right-angled triangle $XYZ$ where angle $Y$ is the right angle. 2. **Identify the sides:** The hypotenuse is $XZ = 16$ cm, and one leg is $ZY = 5$ cm. We want to find the other leg $XY$. 3. **Formula used:** Pythagoras' theorem states that in a right triangle, $$XZ^2 = XY^2 + ZY^2$$ 4. **Substitute known values:** $$16^2 = XY^2 + 5^2$$ 5. **Calculate squares:** $$256 = XY^2 + 25$$ 6. **Isolate $XY^2$:** $$XY^2 = 256 - 25$$ $$XY^2 = 231$$ 7. **Find $XY$ by taking the square root:** $$XY = \sqrt{231}$$ 8. **Calculate the square root:** $$XY \approx 15.1987$$ 9. **Round to 1 decimal place:** $$XY \approx 15.2$$ **Final answer:** The length of $XY$ is approximately $15.2$ cm.