In geometry, we know triangles as 2D closed shapes that have three sides measuring the same or different or three angles of the same or different measurement. If a triangle has one of its angles measuring more than 90 degrees, it is known as an obtuse triangle. Depending on the length, properties, and angles, triangles are categorized into different types: scalene triangle, right triangle, obtuse triangle, acute triangle, isosceles triangle, and equilateral triangle.
If a triangle has one of its three vertex angles measuring more than 90 degrees, then that triangle is considered an obtuse-angled triangle or an obtuse triangle. If one of the angles is obtuse then the other two angles are acute. This means, that when one angle measures greater than 90 degrees, then the sum of the rest two equals less than 90 degrees, which makes the two angles acute. The length of the side that is opposite the obtuse angle is considered the longest.
An obtuse triangle can never be an equilateral triangle, but it can be either scalene or isosceles triangle. Since in an equilateral triangle, all the angles and sides are of equal measurement, therefore, an obtuse-angled triangle can not be an equilateral one. Similarly, a triangle can not be an obtuse triangle and a right triangle simultaneously, since, in a right-angled triangle, one of its angles has to be 90 degrees, which is not possible in the case of an obtuse triangle. Hence, a right-angled triangle can never be an obtuse triangle and vice versa.
Obtuse Angled Triangle Formula
To calculate the perimeter or area of an obtuse-angled triangle, we have two separate formulas. Let us look into the formulas and how to apply them:
Perimeter
The sum of the measures of all the three sides of an obtuse triangle is known as its perimeter. Therefore, the following is the formula to calculate the perimeter of an obtuse triangle:
The perimeter of an obtuse-angled triangle = (a+b+c) units, given that the three sides of the triangle are named a, b, and c.
Area
First of all, a perpendicular has to be drawn outside the triangle to the base. Thus, the height of the triangle is obtained. Once, we find out the height, we can apply the formula given below and find out the area of the triangle.
Area of an obtuse-angled triangle = ½ × b × h
Given that, b is the base of the triangle, and h is the height which is obtained by constructing the perpendicular.
Properties of an Obtuse-Angled Triangle
Every triangle has its own unique set of properties that define them:
- In an obtuse triangle, the side that is opposite to the angle measuring more than 90 degrees, is the longest.
- Such a triangle can have only one obtuse angle, or only one angle measuring greater than 90 degrees. A triangle can never have more than one angle measuring more than 90 degrees since the sum of all the angles of a triangle has to be 180 degrees and not more than that.
- The sum of the rest of the two angles measures less than 90 degrees.
- The orthocenter and the circumcenter of an obtuse triangle lie outside the triangle.
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