Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![### Question 12: Circle Geometry Problem
**Problem Statement:**
Find the length of arc \( \overset{\frown}{JK} \). Round your answer to the nearest tenth.
**Diagram Explanation:**
The diagram consists of a circle with center \( M \). In the circle:
- \( L, J, \) and \( K \) are points on the circumference.
- \( \angle JMK \) is \( 70^\circ \).
- The radius of the circle \( ML \) is labeled as 3 inches.
**Instructions:**
To solve for the length of arc \( \overset{\frown}{JK} \), follow the steps below:
1. **Calculate the Circumference of the Circle:**
The formula for the circumference \( C \) of a circle is given by:
\[
C = 2 \pi r
\]
where \( r \) is the radius of the circle.
2. **Calculate the Fraction of the Circle Represented by Arc \( \overset{\frown}{JK} \):**
The fraction is determined by the angle at the center \( \angle JMK \) as a part of the full circle:
\[
\frac{\theta}{360^\circ}
\]
where \( \theta \) is the central angle of the arc.
3. **Calculate the Length of Arc \( \overset{\frown}{JK} \):**
The length \( L \) of arc \( \overset{\frown}{JK} \) can be found using the formula:
\[
L = \left( \frac{\theta}{360^\circ} \right) \times C
\]
Apply these formulas to find the answer, and round the result to the nearest tenth.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8c8a549a-ce13-4c73-8e46-ff62e8d935c2%2F35b7c205-984c-4501-8350-74d3f229a717%2Fpra1t4r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 12: Circle Geometry Problem
**Problem Statement:**
Find the length of arc \( \overset{\frown}{JK} \). Round your answer to the nearest tenth.
**Diagram Explanation:**
The diagram consists of a circle with center \( M \). In the circle:
- \( L, J, \) and \( K \) are points on the circumference.
- \( \angle JMK \) is \( 70^\circ \).
- The radius of the circle \( ML \) is labeled as 3 inches.
**Instructions:**
To solve for the length of arc \( \overset{\frown}{JK} \), follow the steps below:
1. **Calculate the Circumference of the Circle:**
The formula for the circumference \( C \) of a circle is given by:
\[
C = 2 \pi r
\]
where \( r \) is the radius of the circle.
2. **Calculate the Fraction of the Circle Represented by Arc \( \overset{\frown}{JK} \):**
The fraction is determined by the angle at the center \( \angle JMK \) as a part of the full circle:
\[
\frac{\theta}{360^\circ}
\]
where \( \theta \) is the central angle of the arc.
3. **Calculate the Length of Arc \( \overset{\frown}{JK} \):**
The length \( L \) of arc \( \overset{\frown}{JK} \) can be found using the formula:
\[
L = \left( \frac{\theta}{360^\circ} \right) \times C
\]
Apply these formulas to find the answer, and round the result to the nearest tenth.
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