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In this geometric setup, I'm trying to find an expression for A dependent on , given that and are known.
My take on this is to write the two expressions for the two sides and
and an expression for
Then it seems that I could achieve my goal by eliminating and in the equation for .
Summation of 1) and 2) gives
and multiplication of 1) and 2) gives
Inserting 4) into 3) and squaring provides
Equating 5) and 6) gives an equation dependent on only and
I have a hard time believing this expression to be true because of the following reasoning:
As is increased I would assume that should also increase (relative to ). However, for the numerical values that I have used to test the expression in 10) I find that decreases.
Looking back, I can't find out where I go wrong.