1. **State the problem:** We have a right triangle with one leg $x$, another leg 25 cm, and an angle of 48° opposite the 25 cm side. We need to find the length $x$ to the nearest centimetre. 2. **Identify the sides relative to the angle:** The side opposite the 48° angle is 25 cm, and the side adjacent to the 48° angle is $x$. 3. **Use the tangent function:** In a right triangle, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$. 4. **Set up the equation:** $$\tan(48^\circ) = \frac{25}{x}$$ 5. **Solve for $x$:** $$x = \frac{25}{\tan(48^\circ)}$$ 6. **Calculate $\tan(48^\circ)$:** $$\tan(48^\circ) \approx 1.1106$$ 7. **Substitute and simplify:** $$x = \frac{25}{1.1106}$$ 8. **Show cancellation:** $$x = \frac{25}{\cancel{1.1106}} \times \frac{\cancel{1}}{1} = 22.52$$ 9. **Round to the nearest centimetre:** $$x \approx 23 \text{ cm}$$ **Final answer:** $x = 23$ cm (nearest centimetre).