https://file.aiquickdraw.com/mathbot/file/1729134896416qnwbh3rd.jpg

The problem asks to find the length of the arc \( s \) on a circle with a radius of 4 feet intercepted by a central angle of 120°. The formula for the arc length is:

\[
s = r \theta
\]

where:
- \( r \) is the radius of the circle,
- \( \theta \) is the central angle in radians.

To convert degrees to radians, use the formula:

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

1. Convert the angle \( 120^\circ \) to radians:

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

2. Use the arc length formula:

\[
s = r \theta = 4 \times \frac{2\pi}{3} = \frac{8\pi}{3} \approx 8.38 \text{ feet}
\]

Thus, the length of the arc is approximately \( 8.38 \) feet, which matches the third answer choice.

Do you want further details or have any questions?

Here are 5 related questions to expand this concept:
1. How does the arc length formula change if the radius is doubled?
2. What is the arc length for a central angle of \( 90^\circ \) with the same radius?
3. How would you find the area of the sector formed by the same central angle?
4. What is the length of the arc if the central angle was given in radians directly?
5. How does the formula for arc length relate to the circumference of the entire circle?

**Tip:** Always convert angles to radians when working with formulas involving arc length or trigonometry in general.

Find the length of the arc, s, on a circle of radius 4 feet intercepted by a central angle of 120°. (Round your answer to two decimal places.)

Learn how to find the arc length on a circle with a radius of 4 feet and a central angle of 120°. This problem uses geometry and arc length formulas. Suitable for Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation