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Not So Simple Sines (Posted on 2009-12-24) Difficulty: 3 of 5
Analytically prove sin(54)-sin(18) = 1/2

See The Solution Submitted by Brian Smith    
Rating: 4.0000 (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 mid-point 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 2010-01-11 14:57:18
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