Posted by **Stranger** on Monday, March 18, 2013 at 3:39am.

ABCD is a square where M and N are midpoints of AD and CD, respectively. If sin∠MBN=a/b, where a and b are coprime positive integers, what is the value of a+b?

- Trignometry -
**Steve**, Monday, March 18, 2013 at 4:23am
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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