Find the length of the arc on a circle of radius r intercepted by a central angle 𝜃. (Round your answer to two decimal places.)
Radius r	    	Central Angle 𝜃
17 inches	    	120°


To find the length of the arc \( L \) on a circle, you can use the formula:

\[
L = r \times \theta
\]

However, the angle \( \theta \) must be in radians. First, convert the given angle in degrees to radians using the conversion:

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

Given:
- \( r = 17 \, \text{inches} \)
- \( \theta = 120^\circ \)

Convert \( \theta \) to radians:

\[
\theta_{\text{radians}} = 120^\circ \times \frac{\pi}{180} = \frac{2\pi}{3} \, \text{radians}
\]

Now, substitute into the arc length formula:

\[
L = 17 \times \frac{2\pi}{3}
\]

Let's calculate this.

\[
L \approx 17 \times 2.0944 = 35.60 \, \text{inches}
\]

So, the length of the arc is approximately **35.60 inches**.

Would you like further details or clarifications?

Here are some related questions:
1. How do you calculate the circumference of a circle?
2. What is the relation between radians and degrees?
3. How would the arc length change if the angle was doubled?
4. How can you find the area of a sector using a central angle?
5. What is the arc length when the angle is in degrees, not radians?

**Tip:** Always remember to convert degrees to radians when working with formulas involving arc length or sector area.

Find the length of the arc on a circle of radius r intercepted by a central angle 𝜃. (Round your answer to two decimal places.) Radius r: 17 inches, Central Angle 𝜃: 120°.

Find the arc length of a circle with a radius of 17 inches and a central angle of 120 degrees. Learn how to convert degrees to radians and apply the arc length formula to get a result of 35.60 inches. Suitable for high school geometry students.

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