165 5 cm О 165л О 11.458т О 4.583л
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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Question
![## Problem Statement on Circular Arc Length
**Find the LENGTH of the bolded arc (keep in terms of pi).**
**Diagram Explanation:**
- The diagram is of a circle with a radius of 5 cm.
- A sector of the circle is highlighted, and the central angle of this sector is 165°.
**Multiple Choice Options:**
1. \( \ 165\pi \)
2. \( \ 11.458\pi \)
3. \( \ 4.583\pi \)
4. \( \ 5\pi \)
**Solution Explanation:**
To solve for the length of the bolded arc, we can use the formula for arc length:
\[ \text{Arc Length} = \frac{\theta}{360} \times 2\pi r \]
where:
- \(\theta\) is the central angle in degrees (165°)
- \(r\) is the radius of the circle (5 cm).
Substituting the values, we get:
\[ \text{Arc Length} = \frac{165°}{360°} \times 2\pi \times 5 \]
Simplify the fraction:
\[ \text{Arc Length} = \frac{165}{360} \times 10\pi \]
\[ \text{Arc Length} = \frac{33}{72} \times 10\pi \]
\[ \text{Arc Length} = \frac{11}{24} \times 10\pi \]
\[ \text{Arc Length} = \frac{110}{24}\pi \]
\[ \text{Arc Length} \approx 4.583\pi \]
So, the correct choice is:
\[ \ 4.583\pi \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34dbf93a-185c-4522-bbbf-f73f18b87311%2F34a9f54c-1c64-4bf0-a170-135b49062d05%2F2pq8fis_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Problem Statement on Circular Arc Length
**Find the LENGTH of the bolded arc (keep in terms of pi).**
**Diagram Explanation:**
- The diagram is of a circle with a radius of 5 cm.
- A sector of the circle is highlighted, and the central angle of this sector is 165°.
**Multiple Choice Options:**
1. \( \ 165\pi \)
2. \( \ 11.458\pi \)
3. \( \ 4.583\pi \)
4. \( \ 5\pi \)
**Solution Explanation:**
To solve for the length of the bolded arc, we can use the formula for arc length:
\[ \text{Arc Length} = \frac{\theta}{360} \times 2\pi r \]
where:
- \(\theta\) is the central angle in degrees (165°)
- \(r\) is the radius of the circle (5 cm).
Substituting the values, we get:
\[ \text{Arc Length} = \frac{165°}{360°} \times 2\pi \times 5 \]
Simplify the fraction:
\[ \text{Arc Length} = \frac{165}{360} \times 10\pi \]
\[ \text{Arc Length} = \frac{33}{72} \times 10\pi \]
\[ \text{Arc Length} = \frac{11}{24} \times 10\pi \]
\[ \text{Arc Length} = \frac{110}{24}\pi \]
\[ \text{Arc Length} \approx 4.583\pi \]
So, the correct choice is:
\[ \ 4.583\pi \]
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