Answer :
We are given a circle with a radius of
[tex]$$ r = 36.9 \text{ m} $$[/tex]
and a central angle of
[tex]$$ \theta = \frac{8\pi}{5} \text{ radians}. $$[/tex]
Since the problem instructs us to use
[tex]$$ \pi = 3.14, $$[/tex]
we substitute this value into the central angle:
[tex]$$
\theta = \frac{8 \times 3.14}{5}.
$$[/tex]
Calculating the numerator:
[tex]$$
8 \times 3.14 = 25.12,
$$[/tex]
and then dividing by 5:
[tex]$$
\theta = \frac{25.12}{5} = 5.024 \text{ radians}.
$$[/tex]
The formula for the length of an arc intercepted by a central angle in a circle is:
[tex]$$
\text{Arc Length} = r \times \theta.
$$[/tex]
Substitute the known values into the formula:
[tex]$$
\text{Arc Length} = 36.9 \times 5.024.
$$[/tex]
Multiplying these values:
[tex]$$
\text{Arc Length} = 185.3856 \text{ m}.
$$[/tex]
Finally, rounding this value to the nearest hundredth gives:
[tex]$$
\text{Arc Length} \approx 185.39 \text{ m}.
$$[/tex]
Thus, the length of the arc is
[tex]$$\boxed{185.39 \text{ m}}.$$[/tex]
[tex]$$ r = 36.9 \text{ m} $$[/tex]
and a central angle of
[tex]$$ \theta = \frac{8\pi}{5} \text{ radians}. $$[/tex]
Since the problem instructs us to use
[tex]$$ \pi = 3.14, $$[/tex]
we substitute this value into the central angle:
[tex]$$
\theta = \frac{8 \times 3.14}{5}.
$$[/tex]
Calculating the numerator:
[tex]$$
8 \times 3.14 = 25.12,
$$[/tex]
and then dividing by 5:
[tex]$$
\theta = \frac{25.12}{5} = 5.024 \text{ radians}.
$$[/tex]
The formula for the length of an arc intercepted by a central angle in a circle is:
[tex]$$
\text{Arc Length} = r \times \theta.
$$[/tex]
Substitute the known values into the formula:
[tex]$$
\text{Arc Length} = 36.9 \times 5.024.
$$[/tex]
Multiplying these values:
[tex]$$
\text{Arc Length} = 185.3856 \text{ m}.
$$[/tex]
Finally, rounding this value to the nearest hundredth gives:
[tex]$$
\text{Arc Length} \approx 185.39 \text{ m}.
$$[/tex]
Thus, the length of the arc is
[tex]$$\boxed{185.39 \text{ m}}.$$[/tex]