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Math Help - Angle word problem

  1. #1
    Member Veronica1999's Avatar
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    Angle word problem

    Pls find attached work.
    I would really appreciate some help.
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  2. #2
    Member kalyanram's Avatar
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    Re: Angle word problem

    Hi Veronica,
    There seems to be a contradiction in your results. I cannot make it out because your attempt in the first and second halves are cramped into small space. Here is where I find the contradiction.
    You obtained the length of crease x = 16.\surd 3 for \theta = 30 and x(\theta)= 12.cos\theta . sin(2\theta) and substituting \theta = 30 we have x = 12. \frac{\surd 3}{2}. \frac{\surd 3}{2} = 9
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  3. #3
    Member Veronica1999's Avatar
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    Re: Angle word problem

    Then is my crease length of 16 root 3 correct?
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  4. #4
    Member kalyanram's Avatar
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    Re: Angle word problem

    Let the length of the crease be x and width of paper be l
    \angle CAB = \angle BAD = \theta , \angle EBC = 180 - 2.(90 - \theta) = 2\theta
    Now we have DB + BE = l \Rightarrow x.sin\theta + x.sin\theta . cos2\theta = l \Rightarrow x = \frac{l}{sin\theta (1 + cos2\theta)}
    \Rightarrow x = \frac{l}{2.(sin\theta).(cos\theta)^2}

    Now evaluate for minimum of x by differentiating.

    Kalyan.
    Attached Thumbnails Attached Thumbnails Angle word problem-crease.jpg  
    Last edited by kalyanram; July 10th 2011 at 05:59 AM.
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  5. #5
    Member kalyanram's Avatar
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    Re: Angle word problem

    Instead of differentiating x w.r.t \theta try maximizing the function f(\theta) = sin\theta.cos^2 \theta this gives f'(\theta) = cos^3 \theta - 2.sin^2 \theta.cos\theta = 0 this gives us \theta = 90 or tan\theta = \frac{1}{\surd 2} . We take the angle \theta = tan^{-1} (\frac{1}{\surd 2})

    Kalyan.
    Last edited by kalyanram; July 10th 2011 at 10:35 AM.
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