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How to Construct an Acute Triangle. To construct an acute triangle, simple first construct an angle that is less than 90 degrees and greater than 0 degrees. This will create two sides of your triangle. Then cnstruct a third line intersecting your first two, and you have an acute triangle.
In any triangle, two of the interior angles are always acute (less than 90 degrees) , so there are three possibilities for the third angle: 1  Less than 90Â° - all three angles are acute and so the triangle is acute. 2  Exactly 90Â° - it is a right triangle.3  Greater than 90Â° (obtuse): the triangle is an obtuse triangle.n any triangle, two of the interior angles are always acute (less than 90 degrees) , so there are three possibilities for the third angle: 1  Less than 90Â° - all three angles are acute and so the triangle is acute. 2  Exactly 90Â° - it is a right triangle.