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Thread: 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 $\displaystyle x = 16.\surd 3$ for $\displaystyle \theta = 30$ and $\displaystyle x(\theta)$=$\displaystyle 12.cos\theta . sin(2\theta)$ and substituting $\displaystyle \theta = 30$ we have $\displaystyle x = 12. \frac{\surd 3}{2}. \frac{\surd 3}{2} = 9$
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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 $\displaystyle x$ and width of paper be $\displaystyle l$
    $\displaystyle \angle CAB = \angle BAD = \theta , \angle EBC = 180 - 2.(90 - \theta) = 2\theta$
    Now we have $\displaystyle DB + BE = l \Rightarrow x.sin\theta + x.sin\theta . cos2\theta = l \Rightarrow x = \frac{l}{sin\theta (1 + cos2\theta)}$
    $\displaystyle \Rightarrow x = \frac{l}{2.(sin\theta).(cos\theta)^2}$

    Now evaluate for minimum of $\displaystyle x$ by differentiating.

    Kalyan.
    Attached Thumbnails Attached Thumbnails Angle word problem-crease.jpg  
    Last edited by kalyanram; Jul 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 $\displaystyle x$ w.r.t $\displaystyle \theta$ try maximizing the function $\displaystyle f(\theta) = sin\theta.cos^2 \theta$ this gives $\displaystyle f'(\theta) = cos^3 \theta - 2.sin^2 \theta.cos\theta = 0$ this gives us $\displaystyle \theta = 90 $ or $\displaystyle tan\theta = \frac{1}{\surd 2} $. We take the angle $\displaystyle \theta = tan^{-1} (\frac{1}{\surd 2}) $

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