Find the length of the arc shown in red . Leave your answer in terms of PI. The length of the arc is _ m (Simplify your answer . Type exact answer in terms of PI .)

Question

asked Jun 17, 2023 34.8k views

1 Answer

Chrisjleu · Answer 1 · 2023-06-22T14:34:34+0000

The arc length is given by:

$s=r\theta$

where the angle has to be in radians.

Then we have to transform the angle to radians. To do this we use the formula:

$\theta\cdot(\pi)/(180)$

Then our angle in radians is:

$30\cdot(\pi)/(180)=(\pi)/(6)$

Now that we have the angle we plug its value and the radius in the formula:

$s=9\cdot(\pi)/(6)=(3)/(2)\pi$

Therefore the arc length is:

$s=(3)/(2)\pi$