What is Obtuse Triangle?
An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. In an obtuse triangle, if one angle measures more than 90°, then the sum of the remaining two angles is less than 90°.
Here, the triangle ABC is an obtuse triangle, as ∠A measures more than 90 degrees. Since, ∠A is 120 degrees, the sum of ∠B and ∠C will be less than 90° degrees.
In the above triangle, ∠A + ∠B + ∠C = 180° (because of the Angle Sum Property)
Since ∠A = 120°, therefore, ∠B + ∠C= 60°.
Hence, if one angle of the triangle is obtuse, then the other two angles with always be acute.
Some examples of obtuse triangles:
Non-examples of obtuse triangles:
Special facts about obtuse triangle:
An equilateral triangle can never be obtuse. Since an equilateral triangle has equal sides and angles, each angle measures 60°, which is acute. Therefore, an equilateral angle can never be obtuse-angled.
A triangle cannot be right-angled and obtuse angled at the same time. Since a right-angled triangle has one right angle, the other two angles are acute. Therefore, an obtuse-angled triangle can never have a right angle; and vice versa.
The side opposite the obtuse angle in the triangle is the longest.
Obtuse angled triangles in real life:
In our surroundings, we can find many examples of obtuse triangles. Here are some examples:
Triangle shaped roofs
Hangars found in cupboards