Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and c (as equilateral triangle).

Equilateral triangle.

Sides: a = 120   b = 120   c = 120

Area: T = 6235.383290725
Perimeter: p = 360
Semiperimeter: s = 180

Angle ∠ A = α = 60° = 1.04771975512 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 60° = 1.04771975512 rad

Height: ha = 103.9233048454
Height: hb = 103.9233048454
Height: hc = 103.9233048454

Median: ma = 103.9233048454
Median: mb = 103.9233048454
Median: mc = 103.9233048454

Inradius: r = 34.64110161514
Circumradius: R = 69.28220323028

Vertex coordinates: A[120; 0] B[0; 0] C[60; 103.9233048454]
Centroid: CG[60; 34.64110161514]
Coordinates of the circumscribed circle: U[60; 34.64110161514]
Coordinates of the inscribed circle: I[60; 34.64110161514]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120° = 1.04771975512 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 120° = 1.04771975512 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c (as equilateral triangle).

a = 120 ; ; b = 120 ; ; c = 120 ; ;


Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 120 ; ; b = 120 ; ; c = 120 ; ; : Nr. 1

2. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 120+120+120 = 360 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 360 }{ 2 } = 180 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 180 * (180-120)(180-120)(180-120) } ; ; T = sqrt{ 38880000 } = 6235.38 ; ;

5. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6235.38 }{ 120 } = 103.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6235.38 }{ 120 } = 103.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6235.38 }{ 120 } = 103.92 ; ;

6. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 120**2-120**2-120**2 }{ 2 * 120 * 120 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 120**2-120**2-120**2 }{ 2 * 120 * 120 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 120**2-120**2-120**2 }{ 2 * 120 * 120 } ) = 60° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6235.38 }{ 180 } = 34.64 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 120 }{ 2 * sin 60° } = 69.28 ; ;

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