Geometry Lesson 6-7

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Geometry Lesson 6-7

• Arc Length
• Pg. 341

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• The length of AB in circle O is part of the
  circumference of the circle.
• Since AB 60? and 60/360 1/6.
• The length of that arc is 1/6 of the
  circumference of the circle.

B
60?
A
O
5
C
3

• Now, if we take circumference of the circle and
  multiply by 1/6 we will get the length of AB.
• OK, then 1/6 (2?r) 1/6 (2??5) 10?/6 and of
  course we then reduce our fraction to 5?/3.
• If this works for that arc of 60?, then it should
  work for any arc on the circle. That means there
  is a formula to find the length of an arc.

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Formula to find the length of an arc.

• If we let n? to represent the degree of any arc
  and we know that an arc is part of the circle,
  what fraction could we write to represent that
  arc compared to the circle?
• n?/360 This allows us to turn that arc into a
  fraction of the distance around the circle.
• 2?r is the distance around the circle, so.

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Length of an arc formula

• n?/360 ? 2?r
• Ex. 1) Find the length of AB.
• Remember The central angle
• is equal to its minor arc!
• 
  Ans. 16?/3

120?
8
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Ex. 2

• A go-cart racetrack has 100-meter straightaways
  and semicircular ends with diameters of 40
  meters. Calculate the average speed in meters per
  minute of a go-cart if it completes 4 laps in 6
  minutes. Round your answer to the nearest m/min.

100 m
40 m
40 m
100 m
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Ex. 2 cont.

• 1st , lets find the distance of one lap.
• 2(100) ?d or 200 40?
• 2nd , we need the number of laps so we can __?___
  that with the distance of one lap.
• multiply
  4(200 40?) 4(200
  125.6) 4(325.6) 1302.4
• To finish, we have to know how long a lap
  takes and ________ that number into the total
  distance. Divide
• Ans. 1302.6/6
  217m/min.

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Assignment

• Pg. 343 1-8 all and 10.