The orthocenter of an obtuse triangle is located outside the triangle.
To understand why, let’s first define what the orthocenter is. The orthocenter is the point where the three altitudes of a triangle intersect. An altitude of a triangle is a perpendicular line segment drawn from a vertex to the line that contains the opposite side.
In an obtuse triangle, one of the angles is greater than 90 degrees. When you draw the altitudes from the vertices of the triangle, the altitude from the vertex opposite the obtuse angle will not intersect the opposite side of the triangle within the triangle itself. Instead, this particular altitude extends outside the triangle, connecting to the line that contains the opposite side. Consequently, the three altitudes in an obtuse triangle converge at a point that lies outside the triangle.
Thus, the orthocenter’s position provides insight into the overall geometry of the triangle, helping us understand the relationship between angles and their respective altitudes better.