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I've created the following equation that represents a relation-ship among points:

x = d/(d-sin(a)*w) * cos(a)*w

I want to know the angle (a) that satisfies the relation. I got the following result from WolframAlpha:

(1)

a = 2*atan(w*x + sqrt(d^2+w^2-d^2*x^2+w^2*x^2) / d*(w+x) );

OR

(2)

a = 2*atan(w*x - sqrt(d^2+w^2-d^2*x^2+w^2*x^2) / d*(w+x) );

Notice the different in the sign, it's because during the operations it took the square root from both sides to eliminate squares and that operation added the absolute value to one side.

Does anyone have a better idea? OR A simple way to detect which equation to use?

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what are x,d,w...? – Long Mai Apr 10 '12 at 19:37
@Emmanuel: Please consider using LaTeX in your posts. Expressions that I cannot decipher in a simple way give me a headache, and almost automatically I pass the question by. – André Nicolas Apr 10 '12 at 20:03
Sorry, this is what I'm trying to resolve: Solution – Emmanuel Apr 10 '12 at 20:18
You ask for the angle that satisfies the equation, but do you know for a fact that there is only one such angle? Perhaps Wolfram is telling you that there are two angles that satisfy the equation. Have you tried computing some examples with the two formulas to see whether they both work? – Gerry Myerson Apr 11 '12 at 5:00

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