Find the length s of the circular arc. Need Help? Read It
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
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**Educational Content: Calculating the Length of a Circular Arc**
To find the length of the circular arc \( s \), follow these steps:
1. **Formula for Arc Length:**
- The arc length \( s \) can be calculated using the formula:
\[
s = r \theta
\]
where \( r \) is the radius of the circle and \( \theta \) is the central angle in radians.
2. **Given Values:**
- Radius (\( r \)) = 7
- Central angle (\( \theta \)) = \(\frac{5\pi}{6}\)
3. **Calculation:**
- Substitute the given values into the formula:
\[
s = 7 \times \frac{5\pi}{6}
\]
- Perform the multiplication to find the arc length:
\[
s = \frac{35\pi}{6}
\]
4. **Visualization:**
- The diagram illustrates a circle with a central angle of \(\frac{5\pi}{6}\). The arc corresponding to this angle is highlighted in red. The radius of the circle is marked as 7.
**Additional Resource:**
- A button labeled "Need Help? Read it" is available for further assistance.
---
This guidance helps students to understand and calculate the length of an arc using the radius and central angle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d8dbe42-3baa-47ff-b4b7-eb4b5de6fa73%2F1159e884-f096-4bef-a4d5-1781738ecf25%2Fp37o9c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
**Educational Content: Calculating the Length of a Circular Arc**
To find the length of the circular arc \( s \), follow these steps:
1. **Formula for Arc Length:**
- The arc length \( s \) can be calculated using the formula:
\[
s = r \theta
\]
where \( r \) is the radius of the circle and \( \theta \) is the central angle in radians.
2. **Given Values:**
- Radius (\( r \)) = 7
- Central angle (\( \theta \)) = \(\frac{5\pi}{6}\)
3. **Calculation:**
- Substitute the given values into the formula:
\[
s = 7 \times \frac{5\pi}{6}
\]
- Perform the multiplication to find the arc length:
\[
s = \frac{35\pi}{6}
\]
4. **Visualization:**
- The diagram illustrates a circle with a central angle of \(\frac{5\pi}{6}\). The arc corresponding to this angle is highlighted in red. The radius of the circle is marked as 7.
**Additional Resource:**
- A button labeled "Need Help? Read it" is available for further assistance.
---
This guidance helps students to understand and calculate the length of an arc using the radius and central angle.
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