When is a triangle classified as obtuse?

A triangle is classified as an obtuse triangle when it has one angle greater than 90 degrees. This distinguishing characteristic sets obtuse triangles apart from other types of triangles. In an obtuse triangle, the presence of this single angle that exceeds 90 degrees means that the other two angles must each be less than 90 degrees in order to satisfy the fundamental property that the sum of the angles in any triangle must equal 180 degrees.

This definition ensures that an obtuse triangle has a unique geometric form compared to acute triangles, where all angles are less than 90 degrees, and right triangles, where exactly one angle is equal to 90 degrees. The presence of one angle that exceeds the right angle creates a distinct obtuse nature in the triangle’s overall shape and structure.

Understanding these classifications is vital in geometry, as they help in the study of triangle properties, relationships between their sides and angles, and in applications like trigonometry.