Sure! Let's find the arc length for a circle with a given radius and central angle. Here are the steps to solve the problem:
1. Understand the given values:
- Radius ([tex]\( r \)[/tex]) of the circle: [tex]\( 36.9 \)[/tex] meters.
- Central angle ([tex]\( \theta \)[/tex]) in radians: [tex]\( \frac{8 \pi}{5} \)[/tex].
2. Use the formula for the arc length:
The arc length [tex]\( L \)[/tex] of a circle is given by the formula:
[tex]\[
L = r \times \theta
\][/tex]
3. Substitute the known values into the formula:
- [tex]\( r = 36.9 \)[/tex] meters.
- [tex]\( \theta = \frac{8 \pi}{5} \)[/tex] radians.
Using [tex]\( \pi \approx 3.14 \)[/tex], we substitute:
[tex]\[
\theta = \frac{8 \times 3.14}{5} = 5.024 \, \text{radians}
\][/tex]
4. Calculate the arc length:
[tex]\[
L = 36.9 \times 5.024
\][/tex]
[tex]\[
L \approx 185.3856 \, \text{meters}
\][/tex]
5. Round the answer to the nearest hundredth:
[tex]\[
L \approx 185.39 \, \text{meters}
\][/tex]
So, the arc length is approximately [tex]\( 185.39 \)[/tex] meters.
