1. **State the problem:** We need to find the size of angle $YZX$ in triangle $XYZ$, where $\angle X$ is a right angle, $XY = 7.5$ cm, and $ZY = 22.3$ cm. 2. **Identify the sides:** Since $\angle X$ is right, triangle $XYZ$ is right-angled at $X$ with hypotenuse $ZY = 22.3$ cm. 3. **Label the triangle's sides relative to angle $YZX$:** Angle $YZX$ is at vertex $Z$. The side opposite angle $YZX$ is $XY = 7.5$ cm, and the hypotenuse is $ZY = 22.3$ cm. 4. **Use sine function:** $\sin(\angle YZX) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{XY}{ZY} = \frac{7.5}{22.3}$. 5. **Calculate sine value:** $\sin(\angle YZX) = 0.3363$ (rounded to 4 decimal places). 6. **Find the angle using inverse sine:** $\angle YZX = \sin^{-1}(0.3363)$. 7. **Calculate the angle:** $\angle YZX \approx 19.65^\circ$. 8. **Round to 3 significant figures:** $\angle YZX = 19.7^\circ$. **Final answer:** $$\boxed{19.7^\circ}$$