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Acute Triangle

A triangle is a two-dimensional shape which is bounded by three sides.

On the basis of angles, the triangles can be classified into following categories:
  • Acute Triangle
  • Obtuse Triangle
  • Right Triangle
Here, we shall learn about acute triangle.

Acute Triangle:
Acute triangle is a type of triangle which has all three angles as acute angles, i.e. all the angles are measuring less than $90^{\circ}$.

It is also called acute-angled triangle.

An image of acute triangle is shown in the diagram given below:
Acute Triangle
Here, all the angles are seemed to be less than $90^{\circ}$. So, this can be referred as an acute triangle.

Properties of Acute Triangles:
The important properties of acute triangles are as follows:
All angles are less than a right angle.

The cosine rule is as follows:

cos A = $\frac{b^{2}+c^{2}-a^{2}}{2bc}$

In case of acute triangle, all the angle are acute.
$\angle$A < $90^{\circ}$
Therefore, cos A > 0
, we have
$b^{2}+c^{2}-a^{2}$ > 0
$b^{2}+c^{2}$ > $a^{2}$

Therefore, for an acute triangle
$b^{2}+c^{2}$ > $a^{2}$
$a^{2}+b^{2}$ > $c^{2}$
$a^{2}+c^{2}$ > $b^{2}$
where a, b, and c are the sides of a acute triangle.

Types of Acute Triangles:
Acute triangles can be of following types:
  • Acute Equilateral Triangle
  • Acute Isosceles Triangle
  • Acute Scalene Triangle
Acute equilateral triangle as the name suggests is an acute triangle which is equilateral. It means that each side is equal and each angle measures $60^{\circ}$.

Acute isosceles triangle is an acute triangle, whose two sides are equal as well as corresponding angles are equal.

Acute scalene triangle is also an acute triangle with all sides of different measure and eventually all angles are different.

Related Calculators
Area of Triangle Triangle Calculator
Area of a Equilateral Triangle Calculator Area of a Right Triangle Calculator

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