determine the length of an arc with radius r

The length \( L \) of an arc in a circle can be determined using the following formula:

\[
L = r \theta
\]

Where:
- \( r \) is the radius of the circle.
- \( \theta \) is the central angle subtended by the arc (in radians).

If the angle is given in degrees, you can convert it to radians first:

\[
\theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180}
\]

Once you have the angle in radians, you can apply the first formula to find the arc length.

Would you like to go into more details or need any clarifications?

Here are some related questions to explore further:
1. How do you find the central angle given the arc length and radius?
2. How does the arc length change when the radius is doubled?
3. What is the difference between arc length and chord length?
4. Can you calculate arc length without knowing the angle?
5. How do you derive the formula for arc length?

**Tip**: Always remember that the angle must be in radians when using the arc length formula \( L = r \theta \).

Learn how to determine the length of an arc using the radius and central angle. This guide covers the formula L = rθ and explains how to convert angles from degrees to radians. Ideal for students in Grades 9-12 studying geometry and trigonometry.

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