All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Triangular Cubes (Posted on 2004-12-04)

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)

Comments: ( Back to comment list | You must be logged in to post comments.)
 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

 Search: Search body:
Forums (0)