Find the length *s* of the circular arc. (Assume *r* = 4 and 𝜃 = 130°.)

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.

Learn how to calculate the length of a circular arc with radius r = 4 and angle 𝜃 = 130° using the arc length formula. Detailed step-by-step solution provided.

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