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  For angles, the uniform distribution is attractive as, among all distributions on a bounded range, the uniform distribution has maximum entropy, where entropy is defined to be Shannon's information, the expected value of the log of the density. 
  Whatever the distribution of the perimeter, we will get the same probability of an obtuse angle if, given the perimeter, the event "triangle is obtuse" is independent of the distribution of the perimeter. 
  However, it is easier to condition on A. The conditional distribution of B and C given A is normal and the 4 components are all independent. 
 www.math.niu.edu /~rusin/knownmath/97/random.triangle (2868 words) 
