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Question 9

The number of acute angled triangles whose vertices are chosen from the vertices of a rectangular box is

Solution

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Every face of the rectangular box gives four acute triangles whose vertices are the four corners of that face. There are $$6$$ faces, giving $$24$$ such face-triangles, but each acute triangle is counted on three faces because its three edges lie on face diagonals. Thus the number of distinct acute triangles is $$24/3=8$$.

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