Given a circle with center $O$ and radius $r$, and an arc $AB$ that subtends an angle $\theta$ at the center such that the length of arc $AB$ is $s$, what is the radian measure of angle $\theta$?

• A. $\frac{r}{s}$
• B. $\frac{s}{r}$
• C. $\frac{r^2}{s}$
• D. $\frac{s}{r^2}$

Answer: (B)

Verified step by step guidance

1. Recall the formula that relates the length of an arc \(s\) of a circle to the radius \(r\) and the central angle \(\theta\) (in radians):
2. \[ s = r \times \theta \]
3. To find the radian measure of the angle \(\theta\), rearrange the formula to solve for \(\theta\) by dividing both sides by \(r\):
4. \[ \theta = \frac{s}{r} \]
5. This shows that the radian measure of the angle subtended by the arc is the arc length divided by the radius of the circle.
6. Therefore, the correct expression for the radian measure of angle \(\theta\) is \(\frac{s}{r}\).