# If I have a circle with with an arc length of 31 in. and a radius of 12 in., then what is the angle in radians?

Aug 17, 2015

$2.58333 \ldots$ $r a d$.

#### Explanation:

One radian would be the equivalent of talking the circle's radius and pressing it onto the circumference of the circle, curving it.

This circle's radius is 12 inches. So, I need to find how many 12-inch lines to line up along the circle to get a curve that is 31 inches long.

To do this, I can divide 31 by 12. (Remember this is the same as asking "how many 12's are in 31).

The answer is $2 \frac{7}{12}$, or in decimal form, $2.58333 \ldots$