1. The formula for the length of an arc (s) in a circle given the radius (r) and the central angle (θ) in degrees is: \(s = \frac{\theta}{360} \times 2\pi r\).
- For a 45-degree angle with a radius of 5 units: \(s = \frac{45}{360} \times 2 \times \pi \times 5\), which calculates to approximately 3.93 units.
2. For a 60-degree angle with a radius of 5 units: \(s = \frac{60}{360} \times 2 \times \pi \times 5\), which calculates to approximately 5.24 units.
3. For a 90-degree angle with a radius of 5 units: \(s = \frac{90}{360} \times 2 \times \pi \times 5\), which calculates to approximately 7.85 units.
4. For a 120-degree angle with a radius of 5 units: \(s = \frac{120}{360} \times 2 \times \pi \times 5\), which calculates to approximately 10.47 units.
5. For a 95-degree angle with a radius of 5 units: \(s = \frac{95}{360} \times 2 \times \pi \times 5\), which calculates to approximately 8.30 units.
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Step-by-step explanation:
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Answers & Comments
Answer:
【Answer】: 1. 3.93 2. 5.24 3. 7.85 4. 10.47 5. 8.30
【Explanation】:
1. The formula for the length of an arc (s) in a circle given the radius (r) and the central angle (θ) in degrees is: \(s = \frac{\theta}{360} \times 2\pi r\).
- For a 45-degree angle with a radius of 5 units: \(s = \frac{45}{360} \times 2 \times \pi \times 5\), which calculates to approximately 3.93 units.
2. For a 60-degree angle with a radius of 5 units: \(s = \frac{60}{360} \times 2 \times \pi \times 5\), which calculates to approximately 5.24 units.
3. For a 90-degree angle with a radius of 5 units: \(s = \frac{90}{360} \times 2 \times \pi \times 5\), which calculates to approximately 7.85 units.
4. For a 120-degree angle with a radius of 5 units: \(s = \frac{120}{360} \times 2 \times \pi \times 5\), which calculates to approximately 10.47 units.
5. For a 95-degree angle with a radius of 5 units: \(s = \frac{95}{360} \times 2 \times \pi \times 5\), which calculates to approximately 8.30 units.
```
Step-by-step explanation:
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