The radius of a circle is 56.3 m. Find the length of an are of the circle intercepted 5л by a central angle of radians. 6.
The radius of a circle is 56.3 m. Find the length of an are of the circle intercepted 5л by a central angle of radians. 6.
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°.
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![### Problem 14: Arc Length of a Circle
Given:
- The radius of the circle \( r \) is 56.3 meters.
- The central angle \( \theta \) is \( \frac{5\pi}{6} \) radians.
**Question:**
Find the length of an arc of the circle intercepted by the given central angle.
**Solution:**
The arc length \( s \) of a circle can be calculated using the formula:
\[ s = r\theta \]
Where:
- \( s \) is the arc length,
- \( r \) is the radius,
- \( \theta \) is the central angle in radians.
Plugging the given values into the formula:
\[ s = 56.3 \times \frac{5\pi}{6} \]
First, calculate the multiplication inside the equation:
\[ \frac{5\pi}{6} \approx 2.61799 \]
(using \( \pi \approx 3.14159 \))
\[ s = 56.3 \times 2.61799 \]
\[ s \approx 147.4757 \, \text{meters} \]
Therefore, the length of the arc is approximately 147.48 meters.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fce0f29cc-98be-45bb-9fb8-5b9efd247a01%2F6f146572-f6b6-456c-9109-12831e19d593%2F760i3xh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem 14: Arc Length of a Circle
Given:
- The radius of the circle \( r \) is 56.3 meters.
- The central angle \( \theta \) is \( \frac{5\pi}{6} \) radians.
**Question:**
Find the length of an arc of the circle intercepted by the given central angle.
**Solution:**
The arc length \( s \) of a circle can be calculated using the formula:
\[ s = r\theta \]
Where:
- \( s \) is the arc length,
- \( r \) is the radius,
- \( \theta \) is the central angle in radians.
Plugging the given values into the formula:
\[ s = 56.3 \times \frac{5\pi}{6} \]
First, calculate the multiplication inside the equation:
\[ \frac{5\pi}{6} \approx 2.61799 \]
(using \( \pi \approx 3.14159 \))
\[ s = 56.3 \times 2.61799 \]
\[ s \approx 147.4757 \, \text{meters} \]
Therefore, the length of the arc is approximately 147.48 meters.
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