       RE: Trigonometry, sine theorem.

• To: mathgroup at smc.vnet.net
• Subject: [mg30756] RE: [mg30719] Trigonometry, sine theorem.
• From: "David Park" <djmp at earthlink.net>
• Date: Sun, 9 Sep 2001 03:27:04 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Matthias,

Use the Law of Cosines and Solve for Cos[alpha] and then alpha. By rotating
the data for the three sides you can similarly obtain the angles beta and
gamma.

The following output looks better in StandardForm.

data = {75, 67, 117};
Table[(N[ArcCos[(-a^2 + b^2 + c^2)/(2*b*c)] /.
Thread[{a, b, c} -> RotateLeft[data, i]]]/Degree)*
HoldForm[Degree], {i, 0, 2}]
Plus @@ %
{36.80528562828013*HoldForm[Degree],
32.35705100730148*HoldForm[Degree],
110.8376633644184*HoldForm[Degree]}
180.*HoldForm[Degree]

David Park

> -----Original Message-----
> From: Matthias.Bode at oppenheim.de [mailto:Matthias.Bode at oppenheim.de]
To: mathgroup at smc.vnet.net
> Sent: Saturday, September 08, 2001 2:56 AM
> To: mathgroup at smc.vnet.net
> Subject: [mg30756] [mg30719] Trigonometry, sine theorem.
>
>
> Dear Colleagues,
>
> 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.
>
> How?
>
> Best regards,
>
> Matthias Bode
> Sal. Oppenheim jr. & Cie. KGaA
> Koenigsberger Strasse 29
> D-60487 Frankfurt am Main
> GERMANY
> Tel.: +49(0)69 71 34 53 80
> Mobile: +49(0)172 6 74 95 77
> Fax: +49(0)69 71 34 63 80
> E-mail: matthias.bode at oppenheim.de
> Internet: http://www.oppenheim.de
>
>

```

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