1. **Problem statement:** We have a right-angled triangle with one angle $y$ to find. The side opposite angle $y$ is 7 cm, and the side adjacent to angle $y$ is 8 cm. 2. **Formula used:** To find an angle in a right triangle when opposite and adjacent sides are known, use the tangent function: $$\tan(y) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Apply the formula:** $$\tan(y) = \frac{7}{8}$$ 4. **Calculate angle $y$:** Use the inverse tangent (arctan) to find $y$: $$y = \tan^{-1}\left(\frac{7}{8}\right)$$ 5. **Evaluate:** $$y \approx \tan^{-1}(0.875) \approx 41.2^\circ$$ 6. **Answer:** The angle $y$ is approximately $41.2^\circ$ to 1 decimal place. **Note:** The value $0.9^\circ$ given in the prompt seems incorrect based on the triangle sides provided.