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A cute little angle to find (Posted on 2006-01-18) Difficulty: 4 of 5
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

See The Solution Submitted by Jer    
Rating: 3.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 1 of 7
 
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
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