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Not So Simple Sines (
Posted on 20091224
)
Analytically prove sin(54)sin(18) = 1/2
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Submitted by
Brian Smith
Rating:
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(2 votes)
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Is this analytical?
 Comment 3 of 4 
Not exactly analytical – but I can’t resist...
Imagine a regular pentagon ABCDE with unit sides.
Let M be the midpoint of AB.
Let DM cross CE at G (they’re perpendicular).
Let F be the foot of the perpendicular from A to CE.
Then:
Angle EDG = 54 deg and Angle EAF = 18 deg.
EG – EF = FG = AM
therefore
sin 54 – sin 18 = 1/2
Posted by
Harry
on 20100111 14:57:18
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