If the height of a triangle does not belong to it, then this triangle is ..

In a right-angled triangle, two of its heights are its legs, and the base of the third, drawn from the top of the right angle, lies on the hypotenuse.

In an obtuse triangle, only one height drawn from the apex of the obtuse angle belongs to the triangle.

In equilateral and acute-angled triangles, all three heights belong to triangles (since an equilateral triangle is acute-angled). In addition, in an equilateral triangle, the heights are both medians and bisectors of the triangle.

Answer: obtuse.