find expression for one line segment

Attachment 25106

Link to image: http://s8.postimage.org/u5sdrkl79/geometry.png

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

1)

2)

and an expression for

3)

Then it seems that I could achieve my goal by eliminating and in the equation for .

Summation of 1) and 2) gives

4)

and multiplication of 1) and 2) gives

5)

Inserting 4) into 3) and squaring provides

6)

Equating 5) and 6) gives an equation dependent on only and

7)

Rearranging

8)

9)

10)

I have a hard time believing this expression to be true because of the following reasoning:

For then

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.