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Math Help - Find the length of the fold. please

  1. #1
    rcs
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    Find the length of the fold. please

    please help me on this:

    Find the length of the fold. please-167503_1482759481781_1617660985_1110537_3767947_n.jpg

    A 4 by 6 inch paper is folded so that its upper right corner touches
    the midpoint of an opposite side and such that the fold obtained is the
    longer one. Find the length of the fold.
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    Senior Member BAdhi's Avatar
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    change in the diagram

    find the value of AB, \theta
    Attached Thumbnails Attached Thumbnails Find the length of the fold. please-sad.jpg  
    Last edited by BAdhi; January 6th 2011 at 04:57 AM. Reason: attachment attached
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    Quote Originally Posted by rcs View Post
    please help me on this:

    Click image for larger version. 

Name:	167503_1482759481781_1617660985_1110537_3767947_n.jpg 
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    A 4 by 6 inch paper is folded so that its upper right corner touches
    the midpoint of an opposite side and such that the fold obtained is the
    longer one. Find the length of the fold.
    Dear rcs,

    Look at the figure I had drawn. You can obtain the two equations, x+x\cos\theta=4~and~x\sin\theta=3 Solving these you can find x and \theta. Hope you would be able to continue from here.
    Attached Thumbnails Attached Thumbnails Find the length of the fold. please-sp.pdf  
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  4. #4
    rcs
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    how can the theta be solved if it has only one side that has an exact value? x + xsin theta = 4 and xsin theta = 3 ? elimination?
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  5. #5
    Member rtblue's Avatar
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    Take a look at this rcs:

    x+xcosy=4, xsiny=3 - Wolfram|Alpha

    The system of equations can be solved by graphing the individual equations, and looking for an intersection point. There is only one.
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    Quote Originally Posted by rcs View Post
    how can the theta be solved if it has only one side that has an exact value? x + xsin theta = 4 and xsin theta = 3 ? elimination?
    x+x\cos\theta=4~and~x\sin\theta=3

    3\displaystyle\frac{(1+\cos\theta)}{\sin\theta}=4

    3\displaystyle\left(\frac{2\cos^2\frac{\theta}{2}}  {2\sin\frac{\theta}{2}\cos\frac{\theta}{2}}\right)  =4

    \cot\displaystyle\frac{\theta}{2}=\frac{4}{3}

    \theta=36.87^o
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  7. #7
    rcs
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    thank you... i can solve now for the x side. then use other trig function to be able to find the longer side...
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  8. #8
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    Code:
    E           6-b               B
    
    
    
                                 4-a
    
    4
                                  D
                                  
                                  a
    
    F 3-b  A         3            C
    We only need to call on Big Pete Pythagoras:

    My points A and B are same as yours; the "fold line" is ED.
    I'm leaving left side of diagram out: making its length b, so EB = EA = 6-b;
    plus length of AF becomes 3-b.
    Let CD = a; then DB = DA = 4-a

    Right triangle AEF: 4^2 + (3-b)^2 = (6-b)^2 : leads to b = 11/6

    Right triangle ACD: 3^2 + a^2 = (4-a)^2 : leads to a = 7/8

    We can now use right triangle ADE (or BDE) to get fold line ED; using ADE:
    AE = 6-b = 25/6
    AD = 4-a = 25/8
    ED = SQRT[(25/6)^2 + (25/8)^2] = 125/24 : 5.208333333......
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  9. #9
    Senior Member BAdhi's Avatar
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    My answer is (AB/2)Sec(theta)cosec(theta). AB and theta is as given my diagram
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  10. #10
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    Ok...but no need to use trig functions: triangles (per my diagram) AEF and ACD are SIMILAR.
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