what is the greatest number of acute angle that a triangle can contian?
Well, since there are three angles in a triangle, it has to be 1,2, or 3. Let's start with 3. An equilateral triangle has equal side lengths and angles. Since the sum of the angles of a triangle must equal 180, then each angle is 60 deg, which is acute. So it's possible to have 3 angles in a triangle that are acute.