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

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 \( s = r\theta \).

Learn how to calculate the length of a circular arc using the formula s = r * theta. This problem involves a circle with radius 4 units and an angle of 130 degrees. Discover the step-by-step solution and understand the conversion of degrees to radians. Suitable for high school students.

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