The length of an arc is directly related to its angle measure and the length of its's radius

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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:

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When using radians the following formula applies:

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The area of a sector can also be determined using the radius and degree measure.

The following formula applies when using degree measure:

eq_3_arc_length.png


When using radians the following formula applies:

area_of_sector_radian.png




Here are two examples of how to go about solving an arc length problem:


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Extra Practice:

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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)

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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 pi_over_2_radians.png radians, and forms a resulting arc of approximately 6.28 feet. How long is Mr. T's leg?

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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