1. The problem asks us to find the length of side $YZ$ in a right triangle $XYZ$ where the right angle is at vertex $Y$. 2. According to Pythagoras' theorem, in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. 3. Here, $XZ$ is the hypotenuse with length 16 cm, and the legs are $XY = 9$ cm and $YZ$ (unknown). 4. The formula is $$XZ^2 = XY^2 + YZ^2$$ 5. Substitute the known values: $$16^2 = 9^2 + YZ^2$$ 6. Calculate squares: $$256 = 81 + YZ^2$$ 7. Solve for $YZ^2$: $$YZ^2 = 256 - 81 = 175$$ 8. Take the square root to find $YZ$: $$YZ = \sqrt{175}$$ 9. Simplify the square root: $$\sqrt{175} = \sqrt{25 \times 7} = 5\sqrt{7}$$ 10. Approximate the value: $$YZ \approx 5 \times 2.6458 = 13.229$$ 11. Round to 1 decimal place: $$YZ \approx 13.2$$ Therefore, the length of $YZ$ is approximately 13.2 cm.