The orthocenter of a right triangle is located at the vertex of the right angle.
In any triangle, the orthocenter is defined as the point where the three altitudes intersect. However, in a right triangle, one of the altitudes is coincident with one of the sides of the triangle. Since the right angle already has one of the altitudes along the leg of the triangle, the point of intersection of the other two altitudes will always match the vertex of the right angle. This means that regardless of the sizes of the other two sides, the orthocenter will always be at that specific vertex.