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Math Help - Length of a fold problem

  1. #1
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    Length of a fold problem

    Length of a fold problem-win_20140316_132024.jpg

    I have inserted a picture of the problem here's the text

    The lower right hand corner of a long piece of paper 6" wide is folded over to the left-hand edge as shown. The length L of the fold depends on the angle theta. Show that L=3/sin(theta)cos^2(theta)

    I honestly can't even figure out where to begin with this problem any help would be much appreciated.

    Thanks
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  2. #2
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    Re: Length of a fold problem

    Quote Originally Posted by grelsan View Post
    Click image for larger version. 

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    I have inserted a picture of the problem here's the text

    The lower right hand corner of a long piece of paper 6" wide is folded over to the left-hand edge as shown. The length L of the fold depends on the angle theta. Show that L=3/sin(theta)cos^2(theta)

    I honestly can't even figure out where to begin with this problem any help would be much appreciated.

    Thanks
    Hello,

    I've attached a picture too.

    You have 2 congruent right triangles whose legs are x and y.

    Additionally there is a right triangle with the hypotenuse x and one leg has the length 6'' (in orange).

    You'll get:

    \frac6x = \sin(2 \theta) = 2 \cdot \sin(\theta) \cdot \cos(\theta)~\implies~x = \frac3{\sin(\theta) \cdot \cos(\theta)}

    With the grey right triangle you get:

    \frac xL = \cos(\theta)~\implies~L=\frac x{\cos(\theta)}

    Replace x by the first term:

    \frac xL = \cos(\theta)~\implies~L=\frac {\frac3{\sin(\theta) \cdot \cos(\theta)}}{\cos(\theta)}

    Simplify:

    L=\frac3{\sin(\theta) \cdot \cos^2(\theta)}
    Attached Thumbnails Attached Thumbnails Length of a fold problem-foldlength.png  
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  3. #3
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    Re: Length of a fold problem

    Thanks for the assist! I have to say Im slow or thatsbone devious problem even with yoir excellant explantion it still took me a minute to see everything. Thanks!
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