Obtuse Random Triangles from Three Parts of the Unit Interval

try to draw a new random triangle

Two points are chosen at random in the unit interval. From the resulting three parts, we try to form a triangle. If a triangle can be formed, we are interested in whether it is obtuse or not. It is known that a triangle can be formed with probability 1/4. An obtuse triangle can be formed with probability

9/4-3log(2)

≃

0.170558

. If a triangle can be formed, it is obtuse with probability

9-12log(2)

≃

0.682234

.