1. **State the problem:** We need to find the angle $\theta$ in a right triangle where the side opposite $\theta$ is 4 units and the side adjacent to $\theta$ is 7 units. 2. **Formula used:** To find an angle in a right triangle when opposite and adjacent sides are known, use the tangent function: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 3. **Apply the formula:** $$\tan(\theta) = \frac{4}{7}$$ 4. **Calculate $\theta$:** Take the arctangent (inverse tangent) of both sides: $$\theta = \tan^{-1}\left(\frac{4}{7}\right)$$ 5. **Evaluate the arctangent:** Using a calculator or table, $$\theta \approx \tan^{-1}(0.5714) \approx 29.74^\circ$$ 6. **Round to the nearest degree:** $$\theta \approx 30^\circ$$ **Final answer:** $\boxed{30^\circ}$