Random Numbers, Obtuse Triangles, and π

The probability that two values a and b chosen at random between 0 and 1 will yield an obtuse triangle with side lengths 1, a, and b is . Geometrically, being an obtuse triangle corresponds to the point (a,b) being inside the unit circle but above the line . Another way of stating at this: randomly generate N triangles with side lengths 1, a, and b (with a and b between 0 and 1). If T of them are obtuse, then is approximately π. (Source: Ingenuity in Mathematics by Ross Honsberger.)