Problem: ABCD is a square and M and N are the midpoints of BC and CD respectively. Then sinθ=
Answer Choices:
A. 55
B. 53
C. 510
D. 54
E. none of these answers
Solution:
We may suppose that the sides of the square have length 2, so that BM=ND=1. Then
sinθ=sin(2π−2α)=cos2α=2cos2α−1=2(52)2−1=53
Alternately, one may express Area △AMN in terms of sinθ, find Area △AMN again numerically by subtracting the areas of other (right) triangles from the area of the square, and then solve for sinθ.
