1. **Stating the problem:** We need to create a right-angled triangle XYZ where the side XY = 8 cm, angle XYZ = 90 degrees, and side XZ = 11 cm. 2. **Understanding the triangle:** Since angle XYZ is 90 degrees, point Y is the right angle vertex. Therefore, sides XY and YZ are the legs of the right triangle, and XZ is the hypotenuse. 3. **Using the Pythagorean theorem:** For a right triangle with legs $a$ and $b$, and hypotenuse $c$, the relation is: $$a^2 + b^2 = c^2$$ Here, $XY = 8$ cm, $YZ = ?$, and $XZ = 11$ cm. 4. **Finding side YZ:** Substitute known values: $$8^2 + YZ^2 = 11^2$$ $$64 + YZ^2 = 121$$ 5. **Isolate $YZ^2$:** $$YZ^2 = 121 - 64$$ $$YZ^2 = 57$$ 6. **Calculate $YZ$:** $$YZ = \sqrt{57}$$ $$YZ \approx 7.55 \text{ cm}$$ 7. **Summary:** The triangle has sides XY = 8 cm, YZ approximately 7.55 cm, and hypotenuse XZ = 11 cm with a right angle at Y. **Final answer:** $$YZ \approx 7.55 \text{ cm}$$