Question

Which figure has an orthocenter outside the triangle?

A triangle has angle measures of 30, 75, and 75 degrees.

A triangle has angle measures of 54, 56, and 74 degrees.

A triangle has angle measures of 45, 110, and 25 degrees.

A triangle has angle measures of 90, 48, and 42 degrees.

Answer 1

The orthocenter is inside for acute triangles, on a vertex for right triangles, and outside for obtuse triangles. Only the triangle with angles 45°, 110°, and 25° is obtuse, so its orthocenter lies outside the triangle.