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Triangular Cubes (Posted on 2004-12-04) Difficulty: 2 of 5

Three points have been chosen randomly from the vertices of a cube. What is the probability that they form (a) an acute triangle; (b) a right triangle?

See The Solution Submitted by Erik O.    
Rating: 3.0000 (2 votes)

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re: i c it this way | Comment 5 of 11 |
(In reply to i c it this way by Ady TZIDON)

Right angled triangles can be made not only restricted to one side, but also using as legs one edge and a diagonal of an adjacent side to the two sides that form that edge (not a diagonal of one of the two sides themselves).  The hypotenuse is then a main diagonal of the cube. The sides are in ratio 1:sqrt(2):sqrt(3)

There are 12 edges, and two choices of diagonal for each, so another 24/56 or 3/7 of the cases are like this, leaving only 1/7 for acute triangles.


  Posted by Charlie on 2004-12-05 15:15:44
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