1. **Problem statement:** We have a right-angled triangle with an angle of 20° and the adjacent side to this angle measuring 9 cm. We need to find the length of the side opposite the 20° angle, labeled $x$. 2. **Formula used:** In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Apply the formula:** Here, $\theta = 20^\circ$, opposite side = $x$, adjacent side = 9 cm. $$\tan(20^\circ) = \frac{x}{9}$$ 4. **Solve for $x$:** Multiply both sides by 9: $$x = 9 \times \tan(20^\circ)$$ 5. **Calculate the value:** Using a calculator, $$\tan(20^\circ) \approx 0.36397$$ 6. **Final answer:** $$x = 9 \times 0.36397 = 3.2757 \approx 3.28 \text{ cm}$$ So, the missing side $x$ is approximately 3.28 cm.