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.
[tex]L= \frac{x}{360} * 2 \pi r[/tex]
where * means multiply.
[tex]1= \frac{x}{360} * 3.14 * 9[/tex]
Simplify
[tex]1= \frac{x}{360} *28.26[/tex]
Take the 28.26 over to the other side of the equation, where it then it divides the 1.
[tex] \frac{1}{28.26} = \frac{x}{360} [/tex]
This becomes: [tex]0.035= \frac{x}{360} [/tex]
Then the 360 is brought over to the other side and multiplies the 0.035:
[tex]360*0.035=x[/tex]
And finally simplify the whole equation and we get our answer.
[tex]x=12.739 degrees x=12.7 degrees[/tex]
