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 A cute little angle to find (Posted on 2006-01-18)
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)

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 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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