1. **Problem statement:** We need to find the length of chord AB in a circle with diameter 14, where the angle between the radius line and the chord is 30°. 2. **Given:** Diameter $d = 14$, so radius $r = \frac{d}{2} = 7$. 3. **Understanding the problem:** The chord AB forms an angle $\theta = 30^\circ$ with the radius line from the center to one endpoint of the chord. 4. **Formula for chord length:** The length of a chord can be found using the formula: $$\text{Chord length} = 2r \sin\left(\frac{\alpha}{2}\right)$$ where $\alpha$ is the central angle subtended by the chord. 5. **Relating given angle to central angle:** The angle between the radius and the chord is $30^\circ$, so the central angle $\alpha$ subtended by the chord is twice this angle: $$\alpha = 2 \times 30^\circ = 60^\circ$$ 6. **Calculate chord length:** $$\text{Chord length} = 2 \times 7 \times \sin\left(\frac{60^\circ}{2}\right) = 14 \times \sin(30^\circ)$$ 7. **Evaluate $\sin(30^\circ)$:** $$\sin(30^\circ) = 0.5$$ 8. **Final calculation:** $$\text{Chord length} = 14 \times 0.5 = 7$$ **Answer:** The length of chord AB is $7$ units.