Obtuse Triangle - Definition, Properties

Obtuse Triangle Definition

Let’s explore what is an obtuse triangle?

An obtuse triangle is a type of triangle in which one of the angles is greater than 90 degrees. This characteristic distinguishes it from acute triangles, where all angles are less than 90 degrees, and right triangles, which have one 90-degree angle. The obtuse angle gives the triangle a distinctive ‘stretched’ appearance.

obtuse triangle

Key Properties of Obtuse Triangles

One angle greater than 90 degrees: The defining feature of an obtuse triangle is having one obtuse angle.
The side opposite the obtuse angle is the longest side of the triangle.
The other two angles in an obtuse triangle are always acute (less than 90 degrees).

obtuse triangle definition

Examples of Obtuse Triangles

what is an obtuse triangle

Example 1: A triangle with angles measuring 100 degrees, 40 degrees, and 40 degrees is an obtuse triangle, as one angle is greater than 90 degrees.
Example 2: If a triangle has side lengths of 3 cm, 4 cm, and 6 cm, and the largest angle opposite the 6 cm side is greater than 90 degrees, the triangle is obtuse.

Significance of Obtuse Triangles

Obtuse triangles are important in geometry and trigonometry, especially in studying triangle properties, constructions, and solving problems that involve non-right-angled triangles. They often appear in various real-world applications and geometric designs.