Posted by Stranger on Monday, March 18, 2013 at 3:39am.
If we let x = ∠MBN and y=∠ABM=∠NBC, then
x+2y = pi/2
sin x = sin(pi/2-2y) = cos 2y = 1-2sin^2 y
Now, siny = 1/√5, so
sinx = 1 - 2(1/5) = 3/5
a+b=8
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