To find the length $s$ of a circular arc, you can use the formula:

$s = r \theta$

Where:

• $r$ is the radius of the circle.
• $\theta$ is the angle subtended by the arc at the center of the circle, measured in radians.

First, convert the angle from degrees to radians using the conversion factor $\frac{\pi}{180}$:

$\theta = 130^\circ \times \frac{\pi}{180} = \frac{130\pi}{180} \text{ radians}$

Simplify the angle in radians:

$\theta = \frac{13\pi}{18} \text{ radians}$

Now, plug the values of $r$ and $\theta$ into the arc length formula:

$s = 4 \times \frac{13\pi}{18}$

$s = \frac{52\pi}{18}$

Simplify the fraction:

$s = \frac{26\pi}{9} \text{ units}$

This is the exact value of the arc length. If you want an approximate value, you can calculate:

$s \approx 9.07 \text{ units}$

Would you like any further details or have any questions?

Here are 5 related questions you might find interesting:

1. How would the arc length change if the radius $r$ were doubled?
2. What is the arc length if $\theta = 90^\circ$ and $r = 5$?
3. How do you find the area of the sector formed by the arc and the two radii?
4. Can you calculate the arc length for a complete circle?
5. What happens to the arc length if the angle $\theta$ is given in radians instead of degrees?

Tip: Always ensure that the angle is in radians when using the formula $s = r\theta$.