The distribution function of the distance between two random points in a   right-angled triangle
  In this paper we obtain the density function and the distribution function of the distance between two uniformly and independently distributed random points in any right-angled triangle. The density function is derived from the chord length distribution function using Piefke's formula. We conclude results for random distances between two congruent right-angled triangles together forming a rectangle. 
Uwe B\"asel
math.PR