Given the word problem, we can deduce the following information:
Radius = 6 miles
Central angle = 2 radians
To determine the length of the arc, we use the formula:
[tex]s=r\theta[/tex]
where:
s= arc length
r= radius
θ= central angle in radians
We plug in what we know:
[tex]\begin{gathered} s=r\theta \\ s=(6)(2) \\ \text{Calculate} \\ s=12\text{ miles} \end{gathered}[/tex]
Therefore, the length of the arc is 12 miles.
