1. **State the problem:** We are given a sector OAB of a circle with radius $r=5.9$ mm and area $28$ mm$^2$. We need to find the central angle $\theta$ in degrees, rounded to 1 decimal place. 2. **Formula for the area of a sector:** The area $A$ of a sector with radius $r$ and central angle $\theta$ (in radians) is given by: $$A = \frac{1}{2} r^2 \theta$$ 3. **Rearrange the formula to solve for $\theta$:** $$\theta = \frac{2A}{r^2}$$ 4. **Substitute the known values:** $$\theta = \frac{2 \times 28}{5.9^2} = \frac{56}{34.81}$$ 5. **Calculate the value:** $$\theta = 1.608 \text{ radians (approx)}$$ 6. **Convert radians to degrees:** $$\theta_{\text{degrees}} = \theta \times \frac{180}{\pi} = 1.608 \times \frac{180}{3.1416} = 92.1^\circ$$ 7. **Final answer:** The central angle $\theta$ is approximately **92.1 degrees** to 1 decimal place.