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Trig, point of h base

  1. Sep 15, 2015 #1
    Hello all, was wondering if you fine chaps / ladies could help with a bit of algebra. Annoyed it's had to come to this but alas my algebra levels keep leading me astray.

    c7OPLoi.png

    ## x + y = c ##
    ## x^2 + h^2 = a^2 ##
    ## y^2 + h^2 = b^2 ##

    I've been reading Measurements - Paul Lockhart (wish i picked this up 10 years ago) and the swine asks to first find x and y 'see if you can rearrange the equations to get':

    ## x = c/2 + (a^2 - b^2)/2c ##
    ## y = c/2 - (a^2 - b^2)/2c ##

    After this it is to find h but i would like know the algebra behind finding x and y. I've swapped, rearranged and been all over the place, never the above though. For example,

    ## x^2 - y^2 = a^2 - b^2 ## ==>
    ## -x(x-1) + y^2 + y = c - a^2 - b^2 ## ==> etc,

    trying quadratics, generally leading to nowhere or something else entirely.

    Thanks for any help if given.
     
    Last edited: Sep 15, 2015
  2. jcsd
  3. Sep 15, 2015 #2

    Bystander

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    Hint: x2 - y2 = (x+y)(x-y)
     
  4. Sep 15, 2015 #3
    Oh man, he was going on about Babylonian differences of squares three pages back. o0)

    Cheers Bystander.
     
  5. Sep 15, 2015 #4

    mathman

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    [itex]x^2-y^2=a^2-b^2[/itex]
    [itex]x^2-y^2=(x+y)(x-y)=c(x-y)[/itex]
    therefore [itex]x-y=\frac{a^2-b^2}{c}[/itex]

    You can easily get x and y.
     
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