[itex]s = r \theta[/itex] (i.e. arc-length equals radius times angle) is only true when the angle is expressed in radians.
In other words, we know that [itex]\pi[/itex] is a special number, such that the circumfrence equals [itex]2 \pi r[/itex] for any circle. And so we use radians to make use of this special number.