The length of a circular arc $s$ can be calculated using the formula:

$s = r \cdot \theta$

However, the angle $\theta$ must be in radians. To convert degrees to radians, use the conversion factor:

$\theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180^\circ}$

Given:

• $r = 4$ (radius)
• $\theta = 130^\circ$ (angle in degrees)

First, convert the angle to radians:

$\theta_{\text{radians}} = 130^\circ \times \frac{\pi}{180^\circ} = \frac{130\pi}{180} \text{ radians} = \frac{13\pi}{18} \text{ radians}$

Now, calculate the arc length:

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

Simplifying the expression:

$s = \frac{52\pi}{18} = \frac{26\pi}{9}$

This is the exact length of the arc. If you need a decimal approximation:

$s \approx \frac{26\pi}{9} \approx 9.08 \text{ units}$

So, the length of the circular arc $s$ is approximately 9.08 units.

Would you like more details or have any questions?

Here are 5 related questions you might find useful:

1. How would the arc length change if the radius was doubled?
2. What is the arc length if $\theta = 90^\circ$ and $r = 7$?
3. How do you calculate the sector area of a circle using $r$ and $\theta$?
4. How is the circumference of a circle related to the arc length formula?
5. What happens to the arc length as $\theta$ approaches $360^\circ$?

Tip: Always remember to convert angles from degrees to radians when using them in trigonometric formulas.