Proving the Accuracy of a Car Toe Alignment Tool: Equations and Models Explained

[wrencher]

So I found a web gui for helping do an toe alignment on a car. So I've been looking over the code and I see some equations that I wanted to verify (to make sure the tool is accurate). I drew up one of the models along with the equation, but I can't seem to get phi in terms on only a, b, c, d, and l for the generic case (only when the front/rear track of the car are the same which in the diagram means the trapezoid would be a rectangle). Any help with the proof would be appreciated!

to clarify my bad use of parenthesis:

phi = asin ( (a - b - c + d)/(2*l) )

[PLAIN]http://www.jandlshort.com/pictures/james/alignment/diagram.JPG

 

[wrencher]

Ahhh, I figured it out...of course it was MUCH easier than it seemed to be :).