# Obtuse Random Triangles from Three Parts of the Unit Interval

Obtuse Random Triangles from Three Parts of the Unit Interval

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

9/4-3log(2)

0.170558

9-12log(2)

0.682234