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December 18th, 2018, 08:36 AM   #1
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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.
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December 18th, 2018, 12:46 PM   #2
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Math Focus: Wibbly wobbly timey-wimey stuff.
You can't do it this way unless we know what, geometrically, D is?

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December 18th, 2018, 01:34 PM   #3
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$b+c=160^o$, so you have two equations in two unknowns.
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December 18th, 2018, 02:38 PM   #4
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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.
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December 21st, 2018, 08:47 PM   #5
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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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