POV-Ray : Newsgroups : povray.general : Mathematics question : Re: Mathematics question Server Time
6 Aug 2024 21:40:51 EDT (-0400)
  Re: Mathematics question  
From: Andrea Ryan
Date: 25 Jan 2002 21:11:06
Message: <3C520EB1.D979E5F3@global2000.net>
> Some more information:
> 
> Law of Sines
> sin(Angle1)/Angle1=sin(Angle2)/Angle2=sin(Angle3)/Angle3
> Angle1/sin(Angle1)=Angle2/sin(Angle2)=Angle3/sin(Angle3)
> 
> You can also use the law of cosines but I forget that one right now.

The law of cosines is the more general version of a^2+b^2=c^2.

Here it is:

c^2 = a^2 + b^2 - 2ab * cos C

Where the angle C is the side opposite from the side c.  A and b are the
other
sides.  It works with angles that are not right angles.  If the angle C
is 90
degrees, the term -2ab*cosC disappears because the cosine of 90 degrees
is 0
and you get c^2 = a^2 + b^2.

You could also write the law of cosines as:

a^2 = b^2 + c^2 - 2bc * cos A    where angle A is opposite from side a

and:

b^2 = a^2 + c^2 - 2ac * cos B    where angle B is opposite from side b.

Brendan


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