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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
.
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