Obtuse Triangle

Definition

An obtuse triangle is a figure where one of the three angles measures more than 90°, and the other two angles measure less than 90°.

Properties

1. One of the three interior angles measures more than 90°, and two others are acute angles; in ∆ABC, ∠ABC is the obtuse angle

2. The sum of the two acute angles is always less than the obtuse angle,

so ∠BAC + ∠ACB < ∠ABC

3. The side opposite the obtuse angle is the longest side of the triangle, so AC is the longest side

Types

Obtuse triangles are classified into two types: 1) obtuse scalene triangle, and 2) obtuse isosceles triangles.

The differences between the types are given below:

Formulas

Area (A) = ½ (b × h), where b = base and h = height

Perimeter (P) = a + b + c, where a, b, c are the measures of three sides