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December 18th, 2018, 08:36 AM  #1 
Newbie Joined: Jan 2011 Posts: 8 Thanks: 0  Sine Rule: Can this be solved?
Sorry for the bother... Yeah, it is an elliptical problem. I know I am missing data to complete the use of the Sine Rule to solve it, but I am just wondering if knowing that C+A is already a known value might help. Just I cannot see it. There are other ways to solve it, I know, but I wanted to see if it can be done with the Sine Rule. 
December 18th, 2018, 12:46 PM  #2 
Math Team Joined: May 2013 From: The Astral plane Posts: 2,345 Thanks: 986 Math Focus: Wibbly wobbly timeywimey stuff. 
You can't do it this way unless we know what, geometrically, D is? Dan 
December 18th, 2018, 01:34 PM  #3 
Global Moderator Joined: May 2007 Posts: 6,855 Thanks: 744 
$b+c=160^o$, so you have two equations in two unknowns.

December 18th, 2018, 02:38 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 21,124 Thanks: 2332 
A/sin(20°) = 10/sin(b) = C/sin(c) = (13  A)/sin(160°  b) Eliminating A gives sin(160°  b) = (13/10)sin(b)  sin(20°), which leads to b = 87.0169° approximately. 
December 21st, 2018, 08:47 PM  #5 
Newbie Joined: Jan 2011 Posts: 8 Thanks: 0 
Thank you. Yes, I imagined it came down to a best estimate, I just wondered if I might have been missing something.


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