Question

which figure has an orthocenter outside the triangle?

Explanation:

Step1: Recall orthocenter property

The orthocenter of a triangle is the point of intersection of the triangle's altitudes. It is outside the triangle for an obtuse - angled triangle.

Step2: Identify obtuse - angled triangle

An obtuse - angled triangle has one angle greater than 90°.
The first triangle has angles 30°, 75°, 75° (acute - angled as all angles < 90°).
The second triangle has angles 54°, 56°, 74° (acute - angled as all angles < 90°).
The third triangle has angles 45°, 110°, 25°. Since one angle (110°) > 90°, it is an obtuse - angled triangle.
The fourth triangle has angles 48°, 42°, 90° (right - angled triangle).

Answer:

The triangle with angles 45°, 110°, 25°