Subjects geometry

Arc Length 95926F

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1. **State the problem:** We need to complete the table using the formula for arc length $$s = r\theta$$ where $$r$$ is the radius and $$\theta$$ is the angle in radians. We will calculate the distance $$s$$ for each pair of $$r$$ and $$\theta$$ values. 2. **Formula:** The arc length formula is $$s = r\theta$$. 3. **Given values:** - Radius $$r = 23.0$$ cm - Angle $$\theta = 3\pi/5$$ radians 4. **Calculate $$\theta$$ in decimal:** $$\theta = 3 \times \frac{\pi}{5} = \frac{3\pi}{5} \approx 3 \times 0.628 = 1.885$$ radians (rounded to three significant digits). 5. **Calculate arc length $$s$$:** $$s = r\theta = 23.0 \times 1.885 = 43.355$$ cm 6. **Round to three significant digits:** $$s \approx 43.4$$ cm **Final answer:** The distance $$s$$ is approximately **43.4 cm** for the given radius and angle.