October 5th, 2018, 06:00 AM  #1 
Senior Member Joined: Nov 2011 Posts: 230 Thanks: 2  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, 06:43 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,713 Thanks: 1806 
That possibly wasn't intended.

October 5th, 2018, 06:54 AM  #3 
Senior Member Joined: Nov 2011 Posts: 230 Thanks: 2  ... 
October 5th, 2018, 01:11 PM  #4  
Global Moderator Joined: May 2007 Posts: 6,610 Thanks: 617  Quote:
Last edited by skipjack; October 6th, 2018 at 02:24 AM.  
October 6th, 2018, 01:10 PM  #6 
Global Moderator Joined: May 2007 Posts: 6,610 Thanks: 617 
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 03:11 PM. 
October 6th, 2018, 04:01 PM  #7 
Global Moderator Joined: Dec 2006 Posts: 19,713 Thanks: 1806 
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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