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Answer :
To find the arc length in a circle, you can use the formula:
[tex]\[ \text{Arc length} = \text{radius} \times \text{central angle (in radians)} \][/tex]
We are given:
- The radius of the circle is 36.9 meters.
- The central angle is [tex]\(\frac{8 \pi}{5}\)[/tex] radians.
- Use [tex]\(\pi \approx 3.14\)[/tex].
Let's go through the steps to solve this problem:
1. Convert the central angle to decimal form:
- The central angle given is [tex]\(\frac{8 \pi}{5}\)[/tex].
- Substitute [tex]\(\pi = 3.14\)[/tex] into the central angle:
[tex]\[
\frac{8 \times 3.14}{5} = \frac{25.12}{5} = 5.024
\][/tex]
2. Calculate the arc length:
- Use the formula for arc length:
[tex]\[
\text{Arc length} = 36.9 \, \text{m} \times 5.024
\][/tex]
- Multiply the radius by the central angle:
[tex]\[
\text{Arc length} = 185.3856 \, \text{m}
\][/tex]
3. Round the answer to the nearest hundredth:
- The arc length rounded to the nearest hundredth is 185.39 meters.
Therefore, the arc length is approximately 185.39 meters.
[tex]\[ \text{Arc length} = \text{radius} \times \text{central angle (in radians)} \][/tex]
We are given:
- The radius of the circle is 36.9 meters.
- The central angle is [tex]\(\frac{8 \pi}{5}\)[/tex] radians.
- Use [tex]\(\pi \approx 3.14\)[/tex].
Let's go through the steps to solve this problem:
1. Convert the central angle to decimal form:
- The central angle given is [tex]\(\frac{8 \pi}{5}\)[/tex].
- Substitute [tex]\(\pi = 3.14\)[/tex] into the central angle:
[tex]\[
\frac{8 \times 3.14}{5} = \frac{25.12}{5} = 5.024
\][/tex]
2. Calculate the arc length:
- Use the formula for arc length:
[tex]\[
\text{Arc length} = 36.9 \, \text{m} \times 5.024
\][/tex]
- Multiply the radius by the central angle:
[tex]\[
\text{Arc length} = 185.3856 \, \text{m}
\][/tex]
3. Round the answer to the nearest hundredth:
- The arc length rounded to the nearest hundredth is 185.39 meters.
Therefore, the arc length is approximately 185.39 meters.
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