A triangle is a two-dimensional geometrical figure that consists of three sides and three angles. The sides of a triangle can be of the same or different measurements. The angles of a triangle can be either the same or different. On the basis of different properties, lengths, and angles triangles can be classified into six different types, namely, acute triangle, right triangle, obtuse triangle, scalene triangle, isosceles triangle, and equilateral triangle. An obtuse triangle can be classified as a triangle that consists of an interior angle that is greater than 90 degrees. In this article, we will discuss in detail the obtuse triangle and its different concepts and properties.
What Do You Mean by an Obtuse Triangle?
A triangle is known to be an obtuse triangle or an obtuse-angled triangle when one of its interior vertex angles measures more than 90 degrees. An important thing to note about an obtuse triangle is that it can never be an equilateral triangle. However, it can either be an isosceles triangle or a scalene triangle. Likewise, a triangle cannot be both right-angled as well as obtuse-angled because a right-angle triangle is a triangle in which one angle is 90 degrees and the two angles are acute angles.
Formula to Obtain the Perimeter of an Obtuse Triangle
The perimeter of an obtuse triangle is the sum of all the sides of the triangle. Thus, we have the perimeter of an obtuse triangle as (x + y + z) units where x, y, and z are the sides of the obtuse triangle.
Formula to Obtain the Area of an Obtuse Triangle
The area of an obtuse triangle can be obtained with a formula given by a Greek mathematician, Heron. This formula is also popularly known as Heron’s formula after the name of its inventor. The formula to calculate the area of an obtuse triangle is given below:
s(s- x) (s-y) (s-z), where x, y, and z are the sides of an obtuse triangle and s denotes the semi-perimeter. The formula to calculate the semi-perimeter can be given as: (x + y + z) /2.
Various Properties of Obtuse Triangle
There are various properties of an obtuse triangle. Let us discuss the properties of an obtuse triangle:
- The largest interior angle of an obtuse triangle is opposite to the longest side of the given triangle.
- Any given triangle can have at most one obtuse triangle.
- Since an obtuse angle is an angle of a triangle that measures more than 90 degrees, the other two sides of an obtuse triangle are acute angles which means that they are less than 90 degrees. We can also say that the sum of the other two sides of the triangle is always less than 90 degrees.
An important thing to note about the area of an obtuse triangle is that we can obtain it by drawing a perpendicular line outside the triangle. Then, we can apply the formula that we are very familiar with i.e ½ * Base * Height.
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