In triangle ABC with:
BC = 1;
angle B=45 degrees;
D is on AB such that DC =1;
E and H are on segment AC and EH = 1;
F is on segment AD such that EF=.5;
G is on segment CD;
EFGH is a rectangle.

Find angle A

From triangle GDF:

      |GF|         |GD|
   ---------- = ----------
    sin(135)     sin(GFD)

              or

       1          1-x
   ---------- = --------         (1)
    sin(135)     sin(A) 

From triangle CHG:

   |HG| = |CG|*sin(GCH)

        or

   1/2  = x*sin(45-A)            (2)

Eliminating x from (1) and (2) gives

   1 = [cos(A) - sin(A)]*[sqrt(2) - 2*sin(A)]

Using MathCad I get

   A ~= 7.362315 degrees

Posted by Bractals on 2006-01-18 16:56:42