Find the arc length, s, when r = 2 and 0 = 2.5 radians. S 2.5 2 S= s = [?]
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
Hey what’s the answer to this
![**Finding the Arc Length \( s \)**
This section aims to find the arc length \( s \) of a circle with given parameters.
### Given:
- Radius \( r = 2 \)
- Central angle \( \theta = 2.5 \) radians
### Diagram Explanation:
The diagram represents a circle with a central angle of 2.5 radians and a radius of 2 units. The arc length \( s \) to be found is shown as the curved part between the two points formed by the central angle. The diagram is visually divided to help compute the arc length.
### Formula:
The formula to find the arc length \( s \) is:
\[ s = r \cdot \theta \]
where \( r \) is the radius, and \( \theta \) is the central angle in radians.
### Calculation:
1. Substitute the given values into the formula:
\[ s = 2 \times 2.5 \]
2. Perform the multiplication:
\[ s = 5 \]
### Result:
The arc length \( s \) is \( 5 \) units.
### Interactive Element:
There is an entry box with the label "s = ?" where you can verify your calculation or enter the answer.
---
*Note: Always ensure to use the correct units and double-check your calculations.*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59dc451e-d6f8-4dd4-9faf-549af2b24cc3%2Fefbd99b9-cd2d-499c-bda2-b66730da0162%2F0kf88aa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Finding the Arc Length \( s \)**
This section aims to find the arc length \( s \) of a circle with given parameters.
### Given:
- Radius \( r = 2 \)
- Central angle \( \theta = 2.5 \) radians
### Diagram Explanation:
The diagram represents a circle with a central angle of 2.5 radians and a radius of 2 units. The arc length \( s \) to be found is shown as the curved part between the two points formed by the central angle. The diagram is visually divided to help compute the arc length.
### Formula:
The formula to find the arc length \( s \) is:
\[ s = r \cdot \theta \]
where \( r \) is the radius, and \( \theta \) is the central angle in radians.
### Calculation:
1. Substitute the given values into the formula:
\[ s = 2 \times 2.5 \]
2. Perform the multiplication:
\[ s = 5 \]
### Result:
The arc length \( s \) is \( 5 \) units.
### Interactive Element:
There is an entry box with the label "s = ?" where you can verify your calculation or enter the answer.
---
*Note: Always ensure to use the correct units and double-check your calculations.*
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