Question

Find the measure of the central angle.

the circle has a circumference of 9 and the arc length is 1. Use 3.14 for pie.

Answer 1

To start with we have to write down what we know. pi=3.14, r=9, arc length is 1. x is the angle we are trying to find. Saying that the radius is 9

There is an equation that states that the arc length is equal to x/360 (the fraction of the circle) multiplied by the circumference or 2 times pi times the radius.

`L= (x)/(360) * 2 \pi r`
where * means multiply.

`1= (x)/(360) * 3.14 * 9`
Simplify

`1= (x)/(360) *28.26`
Take the 28.26 over to the other side of the equation, where it then it divides the 1.

`(1)/(28.26) = (x)/(360)`
This becomes:
`0.035= (x)/(360)`
Then the 360 is brought over to the other side and multiplies the 0.035:

`360*0.035=x`
And finally simplify the whole equation and we get our answer.

`x=12.739 degrees x=12.7 degrees`