https://file.aiquickdraw.com/mathbot/file/1730130414167pqsinvpo.jpg

To solve this problem, let's go step-by-step:

### Formula for Arc Length:
\[
L = r \theta
\]
where:
- \(L\) is the arc length,
- \(r\) is the radius,
- \(\theta\) is the central angle in **radians**.

### Step 1: Convert the central angle from degrees to radians.
\[
\theta = 120^\circ \times \frac{\pi}{180^\circ} = \frac{2\pi}{3} \, \text{radians}
\]

### Step 2: Apply the formula for arc length.
Given \(r = 5\) inches and \(\theta = \frac{2\pi}{3}\) radians:
\[
L = 5 \times \frac{2\pi}{3} = \frac{10\pi}{3} \, \text{inches}
\]

### Step 3: Identify the correct answer.
From the options provided, the correct answer is:
\[
\boxed{4) \frac{10\pi}{3} \, \text{inches}}
\]

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Would you like more details or have further questions?

Here are five related questions to explore further:
1. How do you convert degrees to radians for any given angle?
2. What is the difference between arc length and sector area?
3. How would the arc length change if the radius were doubled?
4. How is the formula for arc length derived?
5. How do you find the angle of a complete circle in radians?

**Tip:** Always ensure the angle is in radians when using formulas involving circles, such as arc length or sector area.

What's the length of an arc with a central angle of 120° and a radius of 5 inches?

Calculate the arc length of a circle segment with a central angle of 120° and a radius of 5 inches. This problem involves geometry concepts, including arc length, degree-to-radian conversion, and the arc length formula. Perfect for high school students in Grades 9-11.

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