October 5th, 2018, 07:00 AM  #1 
Senior Member Joined: Nov 2011 Posts: 248 Thanks: 3  law of sines
Why the author use the law of sines? What is goal to use it? In the link: https://www.maa.org/external_archive...n/Polygon.html 
October 5th, 2018, 07:43 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,303 Thanks: 1974 
That possibly wasn't intended.

October 5th, 2018, 07:54 AM  #3 
Senior Member Joined: Nov 2011 Posts: 248 Thanks: 3  ... 
October 5th, 2018, 02:11 PM  #4  
Global Moderator Joined: May 2007 Posts: 6,684 Thanks: 659  Quote:
Last edited by skipjack; October 6th, 2018 at 03:24 AM.  
October 6th, 2018, 02:10 PM  #6 
Global Moderator Joined: May 2007 Posts: 6,684 Thanks: 659 
Area formula (radius=1). Split triangle in half (right triangles) altitude $=\cos(\frac{\alpha}{2})$, base$=\sin(\frac{\alpha}{2})$ Area of original triangle $=\cos(\frac{\alpha}{2})\sin(\frac{\alpha}{2}) = \frac{1}{2}\sin(\alpha)$. Last edited by skipjack; October 6th, 2018 at 04:11 PM. 
October 6th, 2018, 05:01 PM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,303 Thanks: 1974 
The half angle identity used above is most easily proved by use of the $\frac12bc\sin(A)$ formula for a triangle's area.


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