1. **State the problem:** We need to find the angle $\theta$ in a right-angled triangle where the side opposite $\theta$ is 3 cm and the side adjacent to $\theta$ is 8 cm. 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:** $$\tan(\theta) = \frac{3}{8}$$ 4. **Find $\theta$ by taking the arctangent (inverse tangent):** $$\theta = \tan^{-1}\left(\frac{3}{8}\right)$$ 5. **Calculate the value:** $$\theta = \tan^{-1}(0.375)$$ Using a calculator, $$\theta \approx 20.556\degree$$ 6. **Round to 1 decimal place:** $$\theta \approx 20.6\degree$$ **Final answer:** $$\boxed{\theta = 20.6\degree}$$