Triangles are among the first thing children learn when they are introduced to geometrical shapes. A triangle is a two-dimensional closed geometrical figure whose sides may or may not be equal. The three angles may also be the same or different. Based on the length of the three sides and the angles they form, triangles can broadly be classified into different types:
Classification of Triangles based on the angles:
- Obtuse Triangle – One of the angles is more than 90°
- Acute Triangle – One of the angles is less than 90°
- Right-angled Triangle – One of the angles is equal to 90°
Classification of Triangles based on the length of the sides:
- Isosceles Triangle- Any two sides of the triangle are equal.
- Scalene triangle – None of the sides of the triangle are equal
- Equilateral Triangle – All three sides of the triangle are equal
Let us discuss these in detail.
What is an Obtuse Triangle?
A triangle that has one angle out of the three angles more than 90° is called an obtuse-angled triangle. It is a well-established fact that the sum of all the angles of a triangle is always equal to 180° irrespective of the type of triangle. It is thus obvious that the other two angles in an obtuse triangle will always be lesser than 90°or acute.
What are the main properties of an Obtuse Triangle?
- The longest side of the obtuse-angled triangle is the one that is opposite to the obtuse angle.
- A triangle can have only one obtuse angle as the overall sum of all angles of a triangle is always equal to 180°.
- The incentre and centroid always lie inside the obtuse triangle.
- The orthocentre and circumcentre always lie outside the obtuse-angled triangle.
- An obtuse triangle always has two acute angles.
How to find whether a triangle is an Obtuse triangle?
The easiest way to find out whether a triangle is obtuse or not is by measuring the angles. If one of the angles is more than 90° it is clear that the triangle is obtuse. Alternatively, if two of the angles are acute, it is again an obtuse triangle. For example, if one of the angles is 130 degrees and the other two angles are 40 degrees and 10 degrees each, it is an obtuse-angled triangle.
We can also find out whether the triangle is obtuse if we know the sides of the triangle. The sum of squares of two sides of an obtuse triangle is always lesser than the third side which is the largest of the three.
Formulae related to Obtuse-angled Triangle
Area of an Obtuse Triangle
The area of an obtuse triangle can be determined by the formula:
Area = 1/2 *b * h
The perimeter of an Obtuse Triangle
The perimeter of an obtuse triangle is equal to the sum of all three sides.
Perimeter= a + b +c
Where a, b, c are the three sides of the obtuse triangle.
Real-life examples of an Obtuse-angled triangle
Triangles can be seen in a variety of things in our surroundings if you observe them. Triangle-shaped roofs are the most common example of obtuse triangles. Another common example is the hanger used for hanging clothes in your cupboard. You are sure to find some more examples if you observe things closely.
Online portals such as Cuemath have detailed information about all the mathematical concepts. You can refer to them or enrol for the classes to get the maximum benefit. A little effort on your part will make these concepts clear to you. Happy learning!