1. **Problem statement:** We need to find the diameter of a bolt circle given the bolt distance (chord length) of 7 cm and the angle between the diameter and the bolt distance line as 67.5°. 2. **Understanding the problem:** The bolt distance is the chord length between two bolt holes on the circle. The diameter is twice the radius of the circle. The angle given is between the diameter and the chord. 3. **Formula and approach:** In a circle, the chord length $c$ relates to the radius $r$ and the central angle $\theta$ subtended by the chord by the formula: $$c = 2r \sin\left(\frac{\theta}{2}\right)$$ Here, the angle between the diameter and the bolt distance line is 67.5°, so the central angle $\theta$ subtended by the chord is twice that, because the diameter bisects the chord angle: $$\theta = 2 \times 67.5^\circ = 135^\circ$$ 4. **Calculate the radius:** Using the chord length formula: $$7 = 2r \sin\left(\frac{135^\circ}{2}\right) = 2r \sin(67.5^\circ)$$ Solve for $r$: $$r = \frac{7}{2 \sin(67.5^\circ)}$$ Calculate $\sin(67.5^\circ)$: $$\sin(67.5^\circ) \approx 0.9239$$ So, $$r = \frac{7}{2 \times 0.9239} = \frac{7}{1.8478} \approx 3.79 \text{ cm}$$ 5. **Calculate the diameter:** $$\text{Diameter} = 2r = 2 \times 3.79 = 7.58 \text{ cm}$$ 6. **Final answer:** Rounded to the nearest tenth, $$\boxed{7.6 \text{ cm}}$$