Acute from Three Random Lengths
Three numbers are drawn independently and uniformly from [0, 1]. What is the probability that they are the side lengths of 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
- An Obtuse Viewing Angle 5.0/10
- Rounding a Ratio 5.0/10
- The Broken Stick 5.0/10
Source: Classic geometric-probability exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.