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Thread: geomertry similar triangles

  1. #1
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    geomertry similar triangles

    geomertry similar triangles-win_20170528_14_32_34_pro.jpgClick image for larger version. 

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    i am stuck on question 13.
    i know both the triangles are similar due to vertically opposite and alternate angles
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  2. #2
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    Re: geomertry similar triangles

    One way to do this, more "algebra" than "geometry" (well, "analytic geometry"), is to set up a coordinate system so that the x-axis is along the ground, the y-axis is along the 4 m post. Then (0, 0) is at the base of the 4 m post. Let "d" be the distance from the base of the 4 m post to the base of the 5 m post. Then the line from the base of the 4 m post to the top of the 5 m post goes through (0, 0) and (d, 5) so has equation y= (5/d)x. The line from the top of the 4 m post to the bottom of the 5 m post goes through (0, 4) to (d, 0) so has equation y= 4- (4/d)x. Those lines intersect when y= (5/d)x= 4- (4/d)x. Multiply by d to get 5x= 4d- 4x. Add 4x to both sides: 9x= 4d. x= (4/9)d. The point of intersection will have height y= (5/d)((4/9)d)= 20/9 m or 2 and 2/9 m.

    It is interesting that the height of the intersection of the two lines is independent of the distance between the two posts.
    Last edited by HallsofIvy; May 28th 2017 at 06:15 AM.
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  3. #3
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    Re: geomertry similar triangles

    Accidental double post.
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    Re: geomertry similar triangles

    thanks
    do you know if there is a geometry way to do it?
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    Re: geomertry similar triangles

    Quote Originally Posted by markosheehan View Post
    thanks
    do you know if there is a geometry way to do it?
    yes, there is ... using proportions of similar triangles

    $\dfrac{1}{a} = \dfrac{5}{b} \implies b = 5a$

    $\dfrac{y}{b} = \dfrac{4-y}{4a} \implies y = \dfrac{20}{9}$
    Attached Thumbnails Attached Thumbnails geomertry similar triangles-similar_triangles.jpg  
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    Re: geomertry similar triangles

    why is the horizontal distance labelled 5a
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    Re: geomertry similar triangles

    Quote Originally Posted by markosheehan View Post
    why is the horizontal distance labelled 5a
    look at the first equation I posted ...
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    Re: geomertry similar triangles

    damn it. Im and idiot
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