1. **State the problem:** We need to find the size of angle $x$ in a right-angled triangle where the vertical side is 7.9 cm and the base is 3.1 cm. 2. **Formula used:** To find an angle in a right triangle when two sides are known, we use the tangent function: $$\tan(x) = \frac{\text{opposite}}{\text{adjacent}}$$ Here, the opposite side to angle $x$ is 7.9 cm and the adjacent side is 3.1 cm. 3. **Calculate tangent:** $$\tan(x) = \frac{7.9}{3.1}$$ 4. **Simplify the fraction:** $$\tan(x) = \frac{\cancel{7.9}}{\cancel{3.1}} \approx 2.5484$$ 5. **Find angle $x$ using arctangent:** $$x = \tan^{-1}(2.5484)$$ 6. **Evaluate angle $x$:** Using a calculator, $$x \approx 68.3^\circ$$ 7. **Final answer:** The size of angle $x$ is approximately **68.3 degrees** to 1 decimal place.