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Math Help - Width when axis is changed

  1. #1
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    Width when axis is changed

    G'day guys,

    Looking for a bit of help with this:

    ImageShack® - Online Photo and Video Hosting

    Buying a new couch, but I can't measure what I need to. Basically it will be turned onto it's side to go through the door, creating a new "width".

    Also, the feet can be taken off in a worse case scenario, taking the original height to approx 40mm less.

    Any help with this would be fantastic.

    I'd say that we can operate under the assumption that the couch is a right angle at the corner, although it might be slightly off.

    Hopefully I explained this properly
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  2. #2
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    Re: Width when axis is changed

    What I did was set up a coordinate system with (0, 0) at the back bottom of the couch, then determine the equation of the yellow line in your picture: it passes through (0, 970) and (930, 600) so has equation y= ((600- 970))/370)x+ 970= -.398x+ 970. The found the equation of the blue line- it passes through (0, 0) and is perpendicular to the yellow line so has slope -(1/(-.398))= 2.51. Its equation is y= 2.51x. They intersect where -.398x+ 970= 2.51x or x= 333. Putting that into y= 2.51x, y= 837. The length of the blue line is \sqrt{333^2+ 837^2}= 901 mm.

    If you take off the feet, the ends of the yellow line will be at (0, 930) and (930, 560) so the equation of the yellow line in this case will be y= ((560- 930)/930)x+ 930= -0.398x+ 930. The equation of the blue line will be y= 2.51x. The lines will intersect where 2.51x= -.398x+ 930 so 2.91x= 930 and x= 319 mm. y= (2.51)(319)= 802 mm. The length of the blue line is \sqrt{319^2+ 802^2}= 864 mm.
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  3. #3
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    Re: Width when axis is changed

    Wow thanks so much for your help. God I hope my estimate of the height of the arm is wrong - the door is 770mm wide. Hopefully the arm is actually lower, giving me a shorter overall width once turned. Uh oh.
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  4. #4
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    Re: Width when axis is changed

    G'day again,

    I actually have some amended measurements RE: this. Unfortunately the salesperson didn't give the exact measurments originally.

    Height at back = 850mm
    Height at front (Floor up to arm) = 560mm
    Legs are exactly 50mm and can be removed.

    I'm really not fantastic with this kind of math, but I will try to figure out using the formulas you already posted.

    Any help though would be so great!
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  5. #5
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    Re: Width when axis is changed

    I got an approx new width of 696mm

    If anyone could check this, or fix it, that would be great.

    Like I said, I'm terrible at maths.
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