1. The problem asks for the size of angle $YXZ$ in a right triangle $YXZ$ where $Z$ is the right angle. 2. Given sides: $YZ = 20$ cm (adjacent to angle $YXZ$), $ZX = 8$ cm (opposite to angle $YXZ$), and right angle at $Z$. 3. We can use the tangent function since $\tan(\angle YXZ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{ZX}{YZ} = \frac{8}{20}$. 4. Calculate: $\tan(\angle YXZ) = 0.4$. 5. Use inverse tangent (arctan) to find $\angle YXZ$: $$\angle YXZ = \tan^{-1}(0.4)$$ 6. Using a calculator: $\tan^{-1}(0.4) \approx 21.80140949^\circ$. 7. Round to 3 significant figures: $\angle YXZ \approx 21.8^\circ$. Final answer: $\boxed{21.8^\circ}$