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Re: Trigonometry, sine theorem.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg30750] Re: [mg30719] Trigonometry, sine theorem.
  • From: BobHanlon at aol.com
  • Date: Sun, 9 Sep 2001 03:26:49 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

In a message dated 2001/9/8 3:18:14 AM, Matthias.Bode at oppenheim.de writes:

>I have a non-special triangle with sides
>
>a = 75mm, b = 67 mm, c = 117 mm.
>
>I just want to calculate the angles alpha, beta, gamma using a/b =
>sin[alpha]/sin[beta] &c. for a/c and b/c.
>
>All my attempts with FindRoot, Solve, including prior TrigToExp
>transformation were nugatory.
>

a = 75; b = 67; c = 117;

FindRoot[{Sin[alpha]/Sin[beta] == a/b, 
    Sin[alpha]/Sin[gamma] == a/c, 
    alpha+beta+gamma == Pi}, 
  {alpha, Pi/3}, {beta, Pi/3}, {gamma, Pi/3}]

{alpha -> 0.6423734163310746, beta -> 0.5647370762223595, 
  gamma -> 1.934482161036359}


Bob Hanlon
Chantilly, VA  USA


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