7.7 Arc Length

1
7.7 Arc Length

• Geometry CP

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What fraction of its circle is each arc?

• Why?
• A full circle measures 360?

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Definition

• The length of an arc (arc length) is some
  fraction of the circumference of its circle. It
  is measured in some unit of length.
• Arc measure is some fraction of 360?
• Arc length ? arc measure

Arc Length is measured in cm, inches, etc. Arc
Measure is in degrees
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Example
No!
Arc length is a fraction of the circumference
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Example
A
B
O

• Length is a fraction of the circumference
• , so AB is of a circle
• C 2 ? r 2 ? (12) 24 ?
• (24 ?) 6 ?
• Therefore AB 6 ? meters

?
90 360
1 4
1 4
1 4
?
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Example

• Length is a fraction of the circumference
• so CED is of circle
• C ? D 8 ? inches
• Length (8 ?) 4 ? inches
• Therefore CED 4 ? inches

?
180 360
1 2
1 2
1 2
?
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Example
E
O
140?
F

• Length is a fraction of the circumference
• Since ltEOF 140? then EF 140?
• so EF is of a circle
• C 2?r 2?(36) 72? feet
• Length (72?) feet 28? feet

?
?
140 360
7 18
7 18
7 18
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Conjecture

• C-74 Arc Length Conjecture
• The length of an arc equals the arc measure
  divided by 360 multiplied by C
• Or
• AL Arc Measure x C (either 2?r or ?D)
• 360

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Example
B
60?
T
A
?

• MltBTA 60? so mBA 120?
• Length C
• Length C (2?(24)) (48?)
• Length 16? cm

120 360
1 3
1 3
1 3
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Example
What is the radius of the circle? Length of ROT
116? meters
?

• AL (Arc measure ? 360) x C
• mROT 360 - 120 240
• of the circumference
• But the arc length is 116? meters
• 116? meters C (2?r)
• 348? meters 4?r
• 87 meters r
• Therefore the radius is 87 meters

?
240 360
2 3
2 3
2 3
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Homework

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