Find the radius of this circle. 10.л 3 2л 3 r r = [?] Enter
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
Hey what’s the answer to this
#### Explanation of the Given Diagram:
The diagram shows a circle with a segment labeled as \( 2\pi / 3 \) which represents the arc length of the circle's sector. Another label \( 10\pi / 3 \) is the length of the circle's circumference, suggesting that it's a part of the calculation process.
#### Formulas to Use:
1. **Circumference \( C \) of a Circle:**
\[ C = 2\pi r \]
2. **Arc Length \( L \) of a Sector:**
\[ L = \theta r \]
where \( \theta \) is the central angle in radians.
Given:
- Arc Length \( L = \frac{2\pi}{3} \)
- Corresponding Central Angle \( \theta = \frac{10\pi}{3} \)
#### Solving Steps:
1. **Determine the Circumference using the given ratio:**
\[ C = \frac{10\pi}{3} \]
2. **From the Circumference formula:**
\[ 2\pi r = \frac{10\pi}{3} \]
3. **Solving for \( r \):**
\[ r = \frac{\frac{10\pi}{3}}{2\pi} \]
\[ r = \frac{10}{6} \]
\[ r = \frac{5}{3} \]
Therefore, the radius \( r \) is:
\[ r = \frac{5}{3} \]
#### Conclusion:
After solving the equation, we find that the radius \( r \) of the circle is \( \frac{5}{3} \).
To confirm your answer, you can click on the "Enter" button provided in the application interface.
---
By breaking down the problem step-by-step, utilizing known formulas, and solving for the required variable, we can effectively find the radius of a circle from given parameters.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59dc451e-d6f8-4dd4-9faf-549af2b24cc3%2F05007a9a-7cfa-4bda-a893-9ae2785d8f27%2Flylenfh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Radius of a Circle
To calculate the radius of the given circle, refer to the diagram provided.
#### Problem Statement:
Find the **radius** of the circle.
#### Explanation of the Given Diagram:
The diagram shows a circle with a segment labeled as \( 2\pi / 3 \) which represents the arc length of the circle's sector. Another label \( 10\pi / 3 \) is the length of the circle's circumference, suggesting that it's a part of the calculation process.
#### Formulas to Use:
1. **Circumference \( C \) of a Circle:**
\[ C = 2\pi r \]
2. **Arc Length \( L \) of a Sector:**
\[ L = \theta r \]
where \( \theta \) is the central angle in radians.
Given:
- Arc Length \( L = \frac{2\pi}{3} \)
- Corresponding Central Angle \( \theta = \frac{10\pi}{3} \)
#### Solving Steps:
1. **Determine the Circumference using the given ratio:**
\[ C = \frac{10\pi}{3} \]
2. **From the Circumference formula:**
\[ 2\pi r = \frac{10\pi}{3} \]
3. **Solving for \( r \):**
\[ r = \frac{\frac{10\pi}{3}}{2\pi} \]
\[ r = \frac{10}{6} \]
\[ r = \frac{5}{3} \]
Therefore, the radius \( r \) is:
\[ r = \frac{5}{3} \]
#### Conclusion:
After solving the equation, we find that the radius \( r \) of the circle is \( \frac{5}{3} \).
To confirm your answer, you can click on the "Enter" button provided in the application interface.
---
By breaking down the problem step-by-step, utilizing known formulas, and solving for the required variable, we can effectively find the radius of a circle from given parameters.
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