# Trig, point of h base

1. Sep 15, 2015

### raining Pete

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.

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

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,

Thanks for any help if given.

Last edited: Sep 15, 2015
2. Sep 15, 2015

### Bystander

Hint: x2 - y2 = (x+y)(x-y)

3. Sep 15, 2015

### raining Pete

Oh man, he was going on about Babylonian differences of squares three pages back.

Cheers Bystander.

4. Sep 15, 2015

### mathman

$x^2-y^2=a^2-b^2$
$x^2-y^2=(x+y)(x-y)=c(x-y)$
therefore $x-y=\frac{a^2-b^2}{c}$

You can easily get x and y.