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anonymous

  • one year ago

Help please.... If the diameter of the circle is 36, what is the length of arc ABC? A. 8 B. 8pi C. 28pi D. 32pi E. 56pi

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  1. anonymous
    • one year ago
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    |dw:1442538379561:dw|

  2. johnweldon1993
    • one year ago
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    Well remember: \[\large s = r\theta\] The arc length is equal to the radius of the circle times the angle given in radians So first, what is the radius? And what is the angle in radians?

  3. anonymous
    • one year ago
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    18

  4. anonymous
    • one year ago
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    what do you mean by the angle in radian?

  5. anonymous
    • one year ago
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    Can you tell me what they mean when they say "An inscribed angle is aways half the central angel."

  6. johnweldon1993
    • one year ago
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    Okay hang on...lets go one by one lol...So first...the "inscribed angle is always half the central angle" Lets look at a circle

  7. johnweldon1993
    • one year ago
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    |dw:1442584881833:dw|

  8. johnweldon1993
    • one year ago
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    |dw:1442584923535:dw|

  9. anonymous
    • one year ago
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    ohhhhh

  10. johnweldon1993
    • one year ago
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    The inscribed angle *According to the Cenntal Angle Theorem* is always equal to HALF the central angle

  11. anonymous
    • one year ago
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    what does that mean?

  12. johnweldon1993
    • one year ago
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    SO If we look again at that formula I gave you \[\large s = r\theta\] S = arc length *What we need r = radius of the circle \(\large \theta\) = the measure of the central angle in radians

  13. anonymous
    • one year ago
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    i've never seen that 0 thing before.

  14. johnweldon1993
    • one year ago
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    \(\large \theta\) = theta = a measure of an angle :)

  15. anonymous
    • one year ago
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    oh ok

  16. johnweldon1993
    • one year ago
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    yeah lol sorry :D Okay so...lets look at your circle |dw:1442585177036:dw|

  17. johnweldon1993
    • one year ago
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    Comparing that to my circle I drew above, it looks like you have the INSCRIBED angle labeled here right? |dw:1442585225131:dw|

  18. johnweldon1993
    • one year ago
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    SO...since that formula \[\large s = r\theta\] Requires the CENTRAL angle...and we have the inscribed...what would be the central angle?

  19. anonymous
    • one year ago
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    |dw:1442585190505:dw|

  20. johnweldon1993
    • one year ago
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    Not quite.. So if r = 18 remember And we have 80 degrees (because remember central is always double the inscribed) We have \[\large s = 18 \times (80 \times (\frac{\pi}{180}))\] \[\large s = 18 \times \frac{4\pi}{9}\] \[\large s = ?\] Does that make sense?

  21. anonymous
    • one year ago
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    the inscribed angle looks bigger than the central angle why is it only half the central angle?

  22. johnweldon1993
    • one year ago
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    It looks bigger?|dw:1442585541996:dw|

  23. anonymous
    • one year ago
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    ohhhhh okay i see

  24. johnweldon1993
    • one year ago
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    Idk if that helped...or made it more confusing...

  25. johnweldon1993
    • one year ago
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    Okay good lol

  26. johnweldon1993
    • one year ago
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    So yeah...look back up to my formula up there...Does it make sense? \[\large s = r\theta\] \[\large s = 18 \times (80 \times \frac{\pi}{180})\]

  27. anonymous
    • one year ago
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    yes

  28. johnweldon1993
    • one year ago
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    Perfect, Also I notice above you had \[\large \frac{{\pi}}{360}\] If you want to use 360 on the bottom...make sure you have 2pi on top...because remember 2pi is 360 degrees

  29. anonymous
    • one year ago
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    2pi is 360 degrees?

  30. johnweldon1993
    • one year ago
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    Indeed |dw:1442585940253:dw|

  31. johnweldon1993
    • one year ago
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    Remember a whole circle is 360 degrees right?

  32. johnweldon1993
    • one year ago
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    If we travel pi units around the circle...we travel halfway around it...or half of the 360 which is 180

  33. johnweldon1993
    • one year ago
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    If we then travel another pi units around....2pi....we have traveled around the whole circle...or 360 degrees

  34. anonymous
    • one year ago
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    ohhhhh

  35. johnweldon1993
    • one year ago
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    Alright cool, so now that we have that all clear simplify my equation down \[\large s = 18 \times (\frac{80\pi}{180})\] \[\large s = 18\times (\frac{4\pi}{9})\] \[\large s = 2\times 4\pi\]

  36. anonymous
    • one year ago
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    |dw:1442586054554:dw|

  37. johnweldon1993
    • one year ago
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    Where is that 36pi term coming from?

  38. anonymous
    • one year ago
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    |dw:1442586190316:dw|

  39. anonymous
    • one year ago
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    36 pi is from the diameter

  40. anonymous
    • one year ago
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    which is the circumference of the whole circle

  41. anonymous
    • one year ago
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    i subtracted the circumference from the central angle

  42. anonymous
    • one year ago
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    Is arc ABC the same as arc AC

  43. johnweldon1993
    • one year ago
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    Well now the only thing is The want the length of arc ABC |dw:1442586432497:dw|

  44. anonymous
    • one year ago
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    |dw:1442586538130:dw|

  45. johnweldon1993
    • one year ago
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    So we found that length already...the 8pi By subtracting the 8pi from the whole circumference...we are actually getting |dw:1442586574680:dw|

  46. anonymous
    • one year ago
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    Yea i think that's what they wanted

  47. anonymous
    • one year ago
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    Is there a reason we have to find the central angle to find the arc length? Couldnt we have found it using the inscribed angle?

  48. anonymous
    • one year ago
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    @johnweldon1993

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