Question

On a circle of radius 6 feet, what angle would subtend an arc of length 6 feet?

Answer 1

Given the word problem, we can deduce the following information:

Radius of a circle = 6 feet

Arc length = 6 feet

To determine the central angle, we use the formula:

`\theta=(L)/(r)((360)/(2\pi))`

where:

L=arc length

r=radius

θ= central angle in degrees

We plug in what we know:

`\begin{gathered} \theta=(L)/(r)((360)/(2\pi)) \\ =(6)/(6)((360)/(2\pi)) \\ \text{Simplify} \\ \theta=(180)/(\pi) \\ \\ \text{Calculate} \\ \theta=57.30\degree \end{gathered}`

Therefore, the angle is 57.30°.