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Calculation can be based on any 3 items above. If no results after click "Calculate" button, then the data provided is impossible to shape a triangle.

What is triangle?

In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices.

The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

Here’s what a triangle looks like:

What is the Formulas for calculating the triangle?

How to calculate the Altitude of a Scalene Triangle?

Given the side a, side b and side c calculate the Altitude of side a (h_a), Altitude of side b (h_b), Altitude of side c (h_c)(Given a, b, c calculate h_a, h_b, h_c)

Altitude of a scalene triangle is given as:

h_a = 2√(s(s-a)(s-b)(s-c)) / a

h_b = 2√(s(s-a)(s-b)(s-c)) / b

h_c = 2√(s(s-a)(s-b)(s-c)) / c

Where a,b,c are the sides of the triangle, and s is the semi perimeter s = (a+b+c)/2

How to calculate the Area of a triangle?

The formula for the area is: Area =a × b × Sin(C) / 2 or

c × b × Sin(A) / 2 or

a × c × Sin(B) / 2

Given the side a, side b and side c, Altitude of side a (h_a), Altitude of side b (h_b), Altitude of side c (h_c) calculate the Area A(Given a, b, c, h_a, h_b, h_c calculate A)

A = a · h_a/2

A = b · h_b/2

A = c · h_c/2

Given the side a, side b and side c calculate the Area A(Given a, b, c calculate A)

A = √(s(s-a)(s-b)(s-c))

Where a,b,c are the sides of the triangle, and s is the semi perimeter s = (a+b+c)/2

How to calculate the perimeter of a triangle?

The formula for the perimeter is: Perimeter of triangle = Length of (side a + side b + side c)

P (perimeter) = a + b + c (sum of the sides of a triangle)

How to calculate the Inradius(Inscribed Circle Radius) of a triangle?

Inradius = a × Sin(C/2) × Sin(B/2) / Cos (A/2) or

b × Sin(A/2) × Sin(C/2) / Cos (B/2) or

c × Sin(A/2) × Sin(B/2) / Cos (C/2)

How to calculate the Circumradius(Circumscribed Circle Radius) of a triangle?

Circumradius = a / ( 2 * sin (A)) or

b / ( 2 * sin (B)) or

c / ( 2 * sin (C))

How to calculate the Angle bisector of a triangle?

Angle bisector of A

2 × b × c × Cos(A/2) / (b + c)

Angle bisector of B

2 × a × c × Cos(B/2) / (a + c)

Angle bisector of C (t_c)

2 × a × b × Cos(C/2) / (a + b)

How to calculate the Median of a triangle?

Median of side a ( m_a )

m_a² = (2 * b² + 2 * c² - a²) / 4

Median of side b ( m_b )

m_b² = (2 * a² + 2 * c² - b²) / 4

Median of side c( m_c )

m_c² = (2 * a² + 2 * b² - c²) / 4

How to calculate the angle of a triangle?

We can calculate the angle of a triangle by Law of Cosines:

a² = b² + c² - 2 × b × c × Cos(A);

b² = a² + c² - 2 × a × c × Cos(B);

c² = b² + a² - 2 × b × a × Cos(C);

What is the Types of Triangles?

On the basis of length of the sides, triangles are classified into three categories:

1. Scalene Triangle: A scalene triangle is a type of triangle, in which all the three sides have different side measures. Due to this, the three angles are also different from each other.

2. Isosceles Triangle: In an isosceles triangle, two sides have equal length. The two angles opposite to the two equal sides are also equal to each other.

3. Equilateral Triangle: An equilateral triangle has all three sides equal to each other. Due to this all the internal angles are of equal degrees, i.e. each of the angles is 60°

On the basis of measurement of the angles, triangles are classified into three categories:

1. Acute Angle Triangle: An acute triangle has all of its angles less than 90°.

2. Right Angle Triangle: In a right triangle, one of the angles is equal to 90° or right angle.

3. Obtuse Angle Triangle: An obtuse triangle has any of its one angles more than 90°.

What are the Properties of a Triangle?

1. Sum of angles of the triangle is equal to 180 degrees.

2. Exterior angles of a triangle add up to 360 degrees.

3. Shortest side is always opposite the smallest angle of a triangle.