Question

In a circle of radius 6 miles, the length of the arc that subtends a central angle of 2 radians.....

Answer 1

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:

`s=r\theta`

where:

s= arc length

r= radius

θ= central angle in radians

We plug in what we know:

`\begin{gathered} s=r\theta \\ s=(6)(2) \\ \text{Calculate} \\ s=12\text{ miles} \end{gathered}`

Therefore, the length of the arc is 12 miles.