Question

If the length of an arc is 6π ft. and the length of the radius is 24 ft., find the measure of the central angle (in radians).

Answer 1

`\theta=(\pi)/(4)`

1) Notice that the length of an arc is given by the following formula:

`L=\theta\cdot r`

2) Notice that this is the formula in radians. Now, we can plug into that the given data:

`\begin{gathered} 6\pi=\theta\cdot24 \\ 24\theta=6\pi \\ (24θ)/(24)=(6\pi)/(24) \\ \theta=(\pi)/(4) \end{gathered}`

Therefore, this is the answer.