A circle with radius r and a central angle θ. Suppose the arc subtending the central angle θ has length 20π meters and the radius is 24 meters, then θ measured in radians is?

To find the central angle \(\theta\) in radians, given the length of the arc \(L = 20\pi\) meters and the radius \(r = 24\) meters, you can use the formula:

\[
L = r \theta
\]

Where:
- \(L\) is the arc length,
- \(r\) is the radius,
- \(\theta\) is the central angle in radians.

Substitute the given values into the formula:

\[
20\pi = 24 \theta
\]

Solve for \(\theta\):

\[
\theta = \frac{20\pi}{24} = \frac{5\pi}{6} \text{ radians}
\]

So, the central angle \(\theta\) is \(\frac{5\pi}{6}\) radians.

Would you like further details or have any questions? Here are some related questions you might be interested in:

1. How to convert \(\theta\) from radians to degrees?
2. What is the relationship between arc length, radius, and central angle?
3. How would the angle \(\theta\) change if the arc length were different?
4. What is the circumference of the entire circle?
5. How to calculate the area of the sector formed by angle \(\theta\)?

**Tip:** The formula \(L = r\theta\) is only valid when \(\theta\) is measured in radians.

Learn how to calculate the central angle θ in a circle when given the arc length of 20π meters and the radius of 24 meters. Understand the formula L = rθ and solve for θ. Suitable for high school students studying circle geometry and arc lengths.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation