1. **Problem statement:** Find the size of angle $XYZ$ in a right triangle with right angle at $X$, side $XZ = 13$ cm, and side $XY = 4$ cm. 2. **Identify the sides relative to angle $XYZ$:** - Angle $XYZ$ is at vertex $Y$. - The side opposite angle $XYZ$ is $XZ$ (13 cm). - The side adjacent to angle $XYZ$ is $XY$ (4 cm). 3. **Use the tangent function:** The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side: $$\tan(\angle XYZ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{XZ}{XY} = \frac{13}{4}$$ 4. **Calculate the angle:** $$\angle XYZ = \tan^{-1}\left(\frac{13}{4}\right)$$ 5. **Evaluate the inverse tangent:** Using a calculator, $$\angle XYZ \approx \tan^{-1}(3.25) \approx 73.7^\circ$$ 6. **Final answer:** The size of angle $XYZ$ is approximately **73.7 degrees** to 1 decimal place.