Obtuse Angled Triangle


A closed two dimensional figure having three sides of either same or different lengths and three angles of same or different angles is called Triangle. There are three types of triangles based on the lengths of their sides and measure of their angles. If one of the angles of the triangle is greater than 90 degree, it is called an Obtuse angled triangle. This is one of the interior angles of a triangle and the rest two angles of that triangle will be acute angles.


There are two other types of triangles other than Obtuse triangle and those are:

  • Right angle triangle ( = 90 degrees)

  • Acute angle Triangle ( Less than 90 degrees)


Three types of Triangles

These triangles are majorly of three types.

  1. Equilateral Triangle - The triangle having all the three sides equal.

  2. Scalene Triangle -  The triangle in which none of the three sides is equal.

  3. Isosceles Triangle - The triangle where any two sides of a triangle are equal.


What is an Obtuse Angles Triangle?

As mentioned above, if one of the angles of a triangle is greater than the other two (>90 degrees) i.e one of the angles is obtuse, that triangle is known as the Obtuse angled triangle. The sum of all the angles of a triangle is always 180 degrees regardless of the type of triangle. This is the reason that the other two angles in an obtuse angles triangle are acute angles.


Difference Between Acute, Obtuse and Right angled triangle

Acute Angle Triangle - If all the three angles of a triangle are less than 90 degrees, it is called the Acute angled Triangle. It Is formed when two line segments are joined in such a way that the angle formed by them is less than 90 degrees.


Obtuse Angle Triangle - If one of the angles in the triangle is more than 90 degree, that triangle is an obtuse angle triangle. It is formed when two line segments are joined in such a way that they form an angle more than 90 degrees.

Right Angle Triangle -  If one of the angles of a triangle is more than 90 degree, it is called Right Angle Triangle. It is formed when the two line segments make an angle of 90 degrees after joining.


Formula of Obtuse Angle Triangle

Area of an obtuse angle triangle = ½ * b * h , where b is the base and h is the height of the triangle.

The area of a triangle can also be found by using Heron's formula

, i.e A = √(S(S-a)(S-b)(S-c)), where s is the semiperimeter of the triangle and a,b,c are the three sides of the triangle.

s = (a+b+c)/2


The perimeter of a triangle is the sum of all the three sides = a +b + c cm


Can you find out if a triangle is an obtuse angled triangle?

Yes, it’s easy to find out whether the triangle is obtuse angled or not. If one of the angles of a triangle is more than 90 degrees and the other two are less than that, it would be an obtuse angled triangle. 

For example - If one of the angles of a triangle is 120 degrees, and the other two angles are 40 degree and 20 degree, this triangle would be an obtuse angled triangle as one of the angles is more than 90 degree, i.e 120 degrees.

There’s also one more way to find whether a triangle is obtuse angled. If the sum of squares  of the two sides of a triangle is lesser than the largest side, it would be an obtuse angled triangle.

So, if a, b and c are the three sides of the obtuse angled triangle, then a2 > b2  + c2


Properties of Obtuse Angled Triangle

  1. The  longest side of the obtuse triangle is the one opposite to the obtuse angle in that triangle.

  2. As one of the angles is greater than 90 degree in an obtuse triangle, so the other two angles will be acute angles.

  3. An obtuse angled triangle will have only one obtuse angle.

  4. In an obtuse triangle, the centroid and incentre will lie inside the triangle and the circumcentre and orthocentre will lie outside the triangle.


Frequently Asked Questions


How do you find the angle of an obtuse triangle?

To calculate the angle of an obtuse triangle, you need to square the lengths of the two sides of the triangle that will intersect to make the obtuse angle and add the squares of them. For example - if the two sides of the triangle are 2 and 4, then squaring them will give 4 and 16.


What Is the meaning of Obtuse Angle Triangles?

Any triangle having measurement of one angle more than the other two angles and greater than 90 degrees is called an Obtuse angle triangle.


Can a right triangle have an obtuse angle?

No, a right triangle cannot be an obtuse triangle as it is equal to 90 degrees and obtuse angle is always greater than 90 degrees.


How many degrees is an obtuse triangle?

An obtuse triangle is greater than 90 degrees. For example : it can be 120 degrees or 100 degrees.