Question

Find the measure of the central angle.

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.
$L= \frac{x}{360} * 2 \pi r$
where * means multiply.
$1= \frac{x}{360} * 3.14 * 9$
Simplify
$1= \frac{x}{360} *28.26$
Take the 28.26 over to the other side of the equation, where it then it divides the 1.
$\frac{1}{28.26} = \frac{x}{360}$
This becomes: $0.035= \frac{x}{360}$
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.
$x=12.739 degrees x=12.7 degrees$