Subjects geometry

Arc Length E32D62

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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, $$\theta$$ is the angle in radians, and $$s$$ is the arc length (distance). We are given some values and need to find the missing ones. 2. **Given values:** - Radius $$r = 80.0$$ cm - Angle $$\theta = 1$$ rad (assumed from context since not given explicitly) - Distance $$s = 192$$ cm (given for some angle) 3. **Find the missing angle $$\theta$$ for $$s = 192$$ cm:** Using $$s = r\theta$$, solve for $$\theta$$: $$\theta = \frac{s}{r}$$ $$\theta = \frac{192}{80.0} = 2.4$$ radians (rounded to three significant digits) 4. **Find the missing distance $$s$$ for $$\theta = 1$$ rad:** Using $$s = r\theta$$: $$s = 80.0 \times 1 = 80.0$$ cm 5. **Summary:** - For $$\theta = 1$$ rad, $$s = 80.0$$ cm - For $$s = 192$$ cm, $$\theta = 2.4$$ rad All answers are rounded to three significant digits as requested.