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Answer :
To find the arc length of a circle, we can use the formula:
[tex]\[ \text{Arc length} = \text{Radius} \times \text{Central angle in radians} \][/tex]
In this problem, we are given:
- Radius of the circle, [tex]\( R = 36.9 \, \text{m} \)[/tex]
- Central angle, [tex]\( \theta = \frac{8 \pi}{5} \, \text{radians} \)[/tex]
We will use [tex]\( \pi \approx 3.14 \)[/tex] as instructed. So, first calculate the central angle:
[tex]\[ \theta = \frac{8 \times 3.14}{5} \][/tex]
Now, calculate the arc length by multiplying the radius by the central angle:
[tex]\[ \text{Arc length} = 36.9 \times \theta \][/tex]
Substitute the value of [tex]\(\theta\)[/tex] into the equation to find the arc length. Once you have calculated the arc length, round the final answer to the nearest hundredth.
Based on this approach, the arc length is approximately:
[tex]\[ \boxed{185.39} \, \text{meters} \][/tex]
This is the length of the arc intercepted by the given central angle in the circle.
[tex]\[ \text{Arc length} = \text{Radius} \times \text{Central angle in radians} \][/tex]
In this problem, we are given:
- Radius of the circle, [tex]\( R = 36.9 \, \text{m} \)[/tex]
- Central angle, [tex]\( \theta = \frac{8 \pi}{5} \, \text{radians} \)[/tex]
We will use [tex]\( \pi \approx 3.14 \)[/tex] as instructed. So, first calculate the central angle:
[tex]\[ \theta = \frac{8 \times 3.14}{5} \][/tex]
Now, calculate the arc length by multiplying the radius by the central angle:
[tex]\[ \text{Arc length} = 36.9 \times \theta \][/tex]
Substitute the value of [tex]\(\theta\)[/tex] into the equation to find the arc length. Once you have calculated the arc length, round the final answer to the nearest hundredth.
Based on this approach, the arc length is approximately:
[tex]\[ \boxed{185.39} \, \text{meters} \][/tex]
This is the length of the arc intercepted by the given central angle in the circle.
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