To find the radian measure of the angle [tex]\(\theta\)[/tex], given that [tex]\(\theta\)[/tex] is the central angle in a circle with radius [tex]\(r\)[/tex] and it cuts off an arc of length [tex]\(s\)[/tex], we will use the relationship between the central angle in radians, the radius, and the arc length. The formula for this relationship is:
[tex]\[
\theta = \frac{s}{r}
\][/tex]
where:
- [tex]\(\theta\)[/tex] is the central angle in radians,
- [tex]\(s\)[/tex] is the arc length,
- [tex]\(r\)[/tex] is the radius of the circle.
Given:
- [tex]\(r = 5\)[/tex] inches,
- [tex]\(s = 10\)[/tex] inches,
we can substitute these values into the formula:
[tex]\[
\theta = \frac{10 \text{ inches}}{5 \text{ inches}}
\][/tex]
Simplifying this expression:
[tex]\[
\theta = \frac{10}{5} = 2
\][/tex]
Thus, the radian measure of the angle [tex]\(\theta\)[/tex] is:
[tex]\[
\theta = 2
\][/tex]
So, the radian measure of angle [tex]\(\theta\)[/tex] is [tex]\(2\)[/tex].
