Question

What is the approximate length of arc s on the circle below? Use 3.14 for pi. Round your answer to the nearest tenth.

Answer 1

`\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ ------\\ r=12\\ \theta =330 \end{cases}\implies s=\cfrac{(330)(\pi )(12)}{180}\implies s=22\pi`

Answer 2

we know that

To find the length of arc S on the circle, use proportion

`(central\ angle)/(360\°)= (arc\ length\ s)/(2\pi r)`

in this problem we have

`central\ angle=330\°\\r=12\ ft\\pi=3.14`

substitute

`(330\°)/(360\°)= (arc\ length\ s)/(2*3.14*12) \\ \\arc\ length\ s= (330\°*2*3.14*12)/(360\°) \\ \\arc\ length\ s= 69.08\ ft`

Round to the nearest tenth

`arc\ length\ s= 69.1\ ft`

therefore

the answer is

`arc\ length\ s= 69.1\ ft`