1. **State the problem:** We have a right triangle ABC with angle $\angle A = 13^\circ$, side $CB = 19$ mm (adjacent to angle A), and side $AB = x$ (opposite to angle A). We need to find $x$. 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, $\theta = 13^\circ$, opposite side $= x$, adjacent side $= 19$ mm. $$\tan(13^\circ) = \frac{x}{19}$$ 4. **Solve for $x$:** Multiply both sides by 19: $$x = 19 \times \tan(13^\circ)$$ 5. **Calculate $\tan(13^\circ)$:** Using a calculator, $$\tan(13^\circ) \approx 0.2309$$ 6. **Find $x$:** $$x = 19 \times 0.2309 = 4.3871$$ 7. **Interpretation:** The value $4.3871$ mm is the length of side $AB$, which is closest to $4.39$ mm. **Note:** The answer choices given (44.86, 84.46, 64.84, 86.68) do not match this calculation, so please verify the problem or units. Based on the given data and standard trigonometry, $x \approx 4.39$ mm. **Final answer:** $$x \approx 4.39 \text{ mm}$$