An Acute Break
A stick of length 1 is broken at two points chosen independently and uniformly at random. What is the probability that the three pieces form an acute triangle (a non-degenerate triangle with all angles less than 90°)? Give an exact closed form, or a decimal rounded to 4 places.
Related problems & prerequisites
Worth solving first
- Acute from Three Random Lengths 6.0/10
- Nearest Wall of a Triangle 6.0/10
- The Broken Stick 5.0/10
Source: Classic geometric-probability exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.