1. **State the problem:** We have a right-angled triangle XYZ with right angle at Y. 2. **Given:** - Horizontal side XY = 8 cm - Hypotenuse XZ = 19 cm - Vertical side YZ = ? (to find) 3. **Formula:** Pythagoras' theorem states that in a right triangle, $$XZ^2 = XY^2 + YZ^2$$ 4. **Rearrange to find YZ:** $$YZ^2 = XZ^2 - XY^2$$ 5. **Substitute values:** $$YZ^2 = 19^2 - 8^2 = 361 - 64 = 297$$ 6. **Calculate YZ:** $$YZ = \sqrt{297}$$ 7. **Simplify and approximate:** $$YZ \approx 17.2337$$ 8. **Round to 1 decimal place:** $$YZ \approx 17.2\text{ cm}$$ **Final answer:** The length of side YZ is approximately 17.2 cm.