165 5 cm О 165л О 11.458т О 4.583л
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.1: Angles
Problem 3E
Related questions
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:
\[ \ 4.583\pi \]
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, trigonometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL