Question

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 .)

Answer 1

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`