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Math Help - Quadrilateral

  1. #1
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    Quadrilateral

    Here's the picture(I know I suck at paint):

    Quadrilateral-geometry1.png

    Any help would be appreciated.
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  2. #2
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    Re: Quadrilateral

    Quote Originally Posted by RuyHayabusa View Post
    Here's the picture(I know I suck at paint):

    Click image for larger version. 

Name:	Geometry1.png 
Views:	15 
Size:	5.2 KB 
ID:	29129

    Any help would be appreciated.
    Hello

    1. I've modified your sketch a little bit (see attachment): I refer to the labels of my sketch.

    2. Use Pythagorian theorem and Cosine rule: You'll get 4 equations:
    • d^2=7^2+y^2
    • d^2=x^2+4^2-2\cdot 4 \cdot x \cdot \cos(60^\circ)
    • s^2=4^2+y^2-2 \cdot 4 \cdot y \cdot \cos(150^\circ)
    • s^2=x^2+7^2-2 \cdot 7 \cdot x \cdot \cos(60^\circ)


    3. With \cos(60^\circ)=\frac12 and \cos(150^\circ)=-\frac12 \cdot \sqrt{3} you'll get rid of the trigonometric functions.

    4. The calculations are really ugly und you'll get many opportunities to make mistakes. For conformation only:
    (x,y,d,s)=(10,3\sqrt{3},2\sqrt{19},\sqrt{79})
    Attached Thumbnails Attached Thumbnails Quadrilateral-viereckseitex.png  
    Thanks from RuyHayabusa
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  3. #3
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    Re: Quadrilateral

    Quote Originally Posted by earboth View Post
    Hello

    1. I've modified your sketch a little bit (see attachment): I refer to the labels of my sketch.

    2. Use Pythagorian theorem and Cosine rule: You'll get 4 equations:
    • d^2=7^2+y^2
    • d^2=x^2+4^2-2\cdot 4 \cdot x \cdot \cos(60^\circ)
    • s^2=4^2+y^2-2 \cdot 4 \cdot y \cdot \cos(150^\circ)
    • s^2=x^2+7^2-2 \cdot 7 \cdot x \cdot \cos(60^\circ)


    3. With \cos(60^\circ)=\frac12 and \cos(150^\circ)=-\frac12 \cdot \sqrt{3} you'll get rid of the trigonometric functions.

    4. The calculations are really ugly und you'll get many opportunities to make mistakes. For conformation only:
    (x,y,d,s)=(10,3\sqrt{3},2\sqrt{19},\sqrt{79})
    Thanks,but I can't go anywhere from d^2=y^2+49=x^2-4x+16 , s^2=x^2-7x+49 = y^2+4*sqrt(3)*y
    A few pointers please?
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  4. #4
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    Re: Quadrilateral

    Quote Originally Posted by RuyHayabusa View Post
    Thanks,but I can't go anywhere from d^2=y^2+49=x^2-4x+16 , s^2=x^2-7x+49 = y^2+4*sqrt(3)*y
    A few pointers please?

    This quadrilateral is a truncated equilateral triangle and a geometric solution leads to x =10 .Truncated section has two parts. A 30-60 -90 triangle and a regular trapozoid
    Thanks from RuyHayabusa
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  5. #5
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    Re: Quadrilateral

    Hi,
    x is 10 as indicated above. A simple solution is given in the attachment:

    Quadrilateral-mhfgeometry37c.png
    Thanks from RuyHayabusa
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  6. #6
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    Re: Quadrilateral

    Just finished it using johng's way, thanks to all who replied!
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