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To solve for the central angle \(\theta\) in radians, we can use the formula:

\[
\theta = \frac{s}{r}
\]

Where:
- \(s\) is the arc length,
- \(r\) is the radius of the circle.

From the given problem:
- \(s = 8 \, \text{m}\),
- \(r = 13 \, \text{m}\).

Now, let's calculate \(\theta\):

\[
\theta = \frac{8}{13}
\]

I'll calculate this and round the answer to the nearest tenth.The central angle \(\theta\) is approximately \(0.6\) radians when rounded to the nearest tenth.

Would you like more details or have any further questions?

Here are five related questions:
1. How would the central angle change if the radius was doubled?
2. What would the arc length be if the central angle was \(1.2\) radians with the same radius?
3. How is the formula for the central angle derived from the definition of radians?
4. What is the relationship between degrees and radians for central angles?
5. How can you find the circumference of the circle using the radius?

**Tip:** Always make sure to use the same units when applying formulas for geometric figures, such as radians and arc length in this case.

A circle has a radius of 13 m. Find the radian measure of the central angle θ that intercepts an arc of length 8 m.

Learn how to calculate the central angle in radians for a circle with a radius of 13 meters and an arc length of 8 meters. This problem covers key geometric concepts and the radian measure formula. Suitable for high school students in Grades 9-10.

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