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Math Help - Angles and Arcs

  1. #1
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    Angles and Arcs

    the diamater of CIRCLE D is 18 units long find the length of each arc for the given angle measure



    (ARC)LM if m<LDM=100

    - (ARC)MN if m<MDN = 80

    - (ARC)KL IF m<KDL=60

    - (ARC)NJK if m<NDK=120

    - (ARC)KLM if <KDM=160

    - (ARC)JK if m<JDK = 50

    Please solve this for me so i can do the 5 other that i have
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  2. #2
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    Read this.
    About halfway down is the formula for arc length.
    Be careful, you must change degrees to radians.
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  3. #3
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    i still dont get it to be hon est
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  4. #4
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    The length of an arc is \ell  = \phi r where \phi is the central angle and r is the radius.
    Now \phi is in radians so you must change to degrees.

    In your question the arc ML is subtended by an angle of 100^o and radius of the circle is r=9.

    Thus the length of the arc ML is (9)\left(\frac{100\pi}{180}\right).
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  5. #5
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    ok looks my teacher did this problem

    the diameter of CIRCLE C is 32 units long find the length of each arc for the given angle measure

    (ARC)DE if m<DCF=100

    she got the anwser 27.93 is she right??
    Attached Thumbnails Attached Thumbnails Angles and Arcs-telmme.png  
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  6. #6
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    It must be m(\angle DC{\color{red}E}) = 100^o .
    If so that is the correct answer.
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  7. #7
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    yeah it is my bad i try to i tried to follow what she did but i get a different answer from what you posted on the problem

    i got 15.70 units

    btw my teacher she got the diameter and mulitplied by pie so that what i did and got that answer..

    here my answers for all the q;s


    -ARC)LM if m<LDM=100

    - (ARC)MN if m<MDN = 80

    - (ARC)KL IF m<KDL=60

    - (ARC)NJK if m<NDK=120

    - (ARC)KLM if <KDM=160

    - (ARC)JK if m<JDK = 50


    - 15.70
    - 12.56
    - 9.42
    - 37.69
    - 31.41
    - 7.85



    i forgot

    100/360 = L/18 then i multiply 18 * 3.14 then 100/360 = L/56.54 cross multiply then 5654/360 = 15.70
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  8. #8
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    sorry for double post but i gotta turn this in today and i was wondering if i got the answers right
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  9. #9
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    Anothe way of looking at it. A circle of diameter 18 has circumference 18\pi and, of course, is an "angle" of measure 360 degrees. The ratio of those is \frac{18\pi}{360}= \frac{\pi}{20}.

    A an angle \theta degrees will cut off an arc of length L in that same ratio:
    \frac{L}{\theta}= \frac{\pi}{20} so

    L= \frac{\pi\theta}{20}.

    Your first, second, third, and sixth are correct. Your fourth and fifth answers are wrong! I don't know how you did that!

    Note that, for the third one, the angle is 60 and you got, correctly, 9.42. The fourth has angle 120, exactly twice the angle in three so the arclength should be 2 times 9.42, which is NOT "37.69" which is 4 times as large.

    Similarly, the angle for the fourth one is 160 degrees, exactly twice the 80 degrees in number 2. The arclength should be 2 times the 12.56 you got for that, not "31.41".
    Last edited by HallsofIvy; July 15th 2009 at 06:02 AM.
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