1. **State the problem:** We need to find the size of angle $x$ in a right triangle with sides 9.7 cm (vertical) and 5.1 cm (horizontal). 2. **Formula used:** To find an angle in a right triangle, we use the tangent function: $$\tan(x) = \frac{\text{opposite}}{\text{adjacent}}$$ Here, opposite side to angle $x$ is 9.7 cm and adjacent side is 5.1 cm. 3. **Calculate tangent:** $$\tan(x) = \frac{9.7}{5.1}$$ 4. **Evaluate the fraction:** $$\tan(x) = 1.901960784$$ 5. **Find angle $x$ using arctangent:** $$x = \tan^{-1}(1.901960784)$$ 6. **Calculate angle $x$:** $$x \approx 62.3^\circ$$ 7. **Final answer:** The size of angle $x$ is approximately **62.3 degrees** to 1 decimal place.