Skip to main content
guest
Join

Help

Sign In
scherer
Home
guest

Join

Help

Sign In
scherer
Wiki Home
Recent Changes
Pages and Files
Members
Home
AP Calculus
Precalculus
Algebra II
Scherer RTMSD
Arc Length
Edit
0
17
…
0
Tags
No tags
Notify
RSS
Backlinks
Source
Print
Export (PDF)
The length of an arc is directly related to its angle measure and the length of its's radius
A = area of sector
C = circumference
Ø = degree of angle
P = center point
S = arc length
r = radius of circle
There are two methods used to solve for the length of an arc, one involving degrees and one involving radian measure.
When using degrees the following formulas apply:
When using radians the following formula applies:
The area of a sector can also be determined using the radius and degree measure.
The following formula applies when using degree measure:
When using radians the following formula applies:
Here are two examples of how to go about solving an arc length problem:
Extra Practice:
6. An arc with angle 76 degrees and radius of 3.4 inches has a sector with what area?
7. Chuck Norris, angered by a parking ticket, roundhouse kicks a nearby pedestrian. If his leg is 3 feet long and the angle formed by his kick is 68°, what is the length of the arc swept out by his kick? (hint, the length of his leg is the radius of the arc)
8. Inspired by Chucks show of manliness, Mr. T decides kick some fool who owes him money. Because he is a beacon of human performance, Mr. T kicks through a full
radians, and forms a resulting arc of approximately 6.28 feet. How long is Mr. T's leg?
Answers to practice problems:
1. 4.32 inches
2. π/3
3. 2.7π/6 meters
4. 4.5π sq feet
5. 1.53 sq feet
6. 2.44π
7. 1.133333 feet
8. 12.56/π
Javascript Required
You need to enable Javascript in your browser to edit pages.
help on how to format text
Turn off "Getting Started"
Home
...
Loading...
A = area of sector
C = circumference
Ø = degree of angle
P = center point
S = arc length
r = radius of circle
There are two methods used to solve for the length of an arc, one involving degrees and one involving radian measure.
When using degrees the following formulas apply:
When using radians the following formula applies:
The area of a sector can also be determined using the radius and degree measure.
The following formula applies when using degree measure:
When using radians the following formula applies:
Here are two examples of how to go about solving an arc length problem: