Obtuse triangle

An obtuse triangle is a triangle that has one obtuse angle (an angle greater than 90°).

The side of this house is in the shape of an obtuse triangle.

Properties of obtuse triangles

Using the Pythagorean Theorem to identify obtuse triangles

For a right triangle with hypotenuse of length c, and legs of lengths a and b, the Pythagorean Theorem states:

a2 + b2 = c2

For any triangle, if a2 + b2 < c2, where c is the longest side, the triangle is an obtuse triangle.

Example:

Is triangle △ABC an obtuse triangle?

Side AB above is the longest side. Plugging this into the Pythagorean Theorem where c = 9 and a and b = 6:

a2 + b2 = 62 + 62 = 72

c2 = 92 = 81

72 < 81

Since a2 + b2 < c2, △ABC is an obtuse triangle with obtuse angle C.