Find the length of the arc intercepted by the following central angle in a circle with the given radius. a = 21°, r=5 centimeters The length of the arc is (Round to three decimal places.) centimeters.
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
![### Problem Statement
Find the length of the arc intercepted by the following central angle in a circle with the given radius.
\( \alpha = 21^\circ \), \( r = 5\) centimeters
The length of the arc is __________ centimeters.
(Round to three decimal places.)
### Instructions
1. **Problem Description**:
- You need to find the length of an arc in a circle.
- The central angle (\(\alpha\)) given is \(21^\circ\).
- The radius (\(r\)) of the circle is \(5\) centimeters.
2. **Calculation**:
- Use the formula for the length of an arc \((s)\):
\[
s = r \cdot \theta
\]
where \(\theta\) is the central angle in radians.
- First, convert the central angle from degrees to radians using the formula:
\[
\theta = \alpha \cdot \frac{\pi}{180^\circ}
\]
Substitute \( \alpha = 21^\circ\):
\[
\theta = 21 \cdot \frac{\pi}{180} = \frac{21\pi}{180} = \frac{7\pi}{60}
\]
- Now calculate the arc length \( (s) \):
\[
s = 5 \cdot \frac{7\pi}{60} \approx 5 \cdot 0.3665 \approx 1.8325
\]
3. **Answer Entry**:
- Enter your answer in the answer box below, rounding to three decimal places:
\[
\text{The length of the arc is } 1.833 \text{ centimeters.}
\]
4. **Final Step**:
- Once you've entered your answer, click "Check Answer" to verify your solution.
### Input Section
- **Answer Box**: Provide your final rounded answer in the answer box.
- **Example Calculation**:
Enter the calculated length of the arc, which is \(1.833\) centimeters.
### Additional Notes
- Make sure the input adheres to the rounding instruction (to three decimal places).
- Ensure all parts are correctly displayed and all steps are visible before submission.
#### Diagram Explanation (if applicable):
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