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 = 51   b = 51   c = 51

Area: T = 1126.266603762
Perimeter: p = 153
Semiperimeter: s = 76.5

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

Height: ha = 44.1677295593
Height: hb = 44.1677295593
Height: hc = 44.1677295593

Median: ma = 44.1677295593
Median: mb = 44.1677295593
Median: mc = 44.1677295593

Inradius: r = 14.72224318643
Circumradius: R = 29.44548637287

Vertex coordinates: A[51; 0] B[0; 0] C[25.5; 44.1677295593]
Centroid: CG[25.5; 14.72224318643]
Coordinates of the circumscribed circle: U[25.5; 14.72224318643]
Coordinates of the inscribed circle: I[25.5; 14.72224318643]

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 = 51 ; ; b = 51 ; ; c = 51 ; ;


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 = 51 ; ; b = 51 ; ; c = 51 ; ; : Nr. 1

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

p = a+b+c = 51+51+51 = 153 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 153 }{ 2 } = 76.5 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 76.5 * (76.5-51)(76.5-51)(76.5-51) } ; ; T = sqrt{ 1268475.19 } = 1126.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1126.27 }{ 51 } = 44.17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1126.27 }{ 51 } = 44.17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1126.27 }{ 51 } = 44.17 ; ;

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{ 51**2-51**2-51**2 }{ 2 * 51 * 51 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 51**2-51**2-51**2 }{ 2 * 51 * 51 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 51**2-51**2-51**2 }{ 2 * 51 * 51 } ) = 60° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1126.27 }{ 76.5 } = 14.72 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 51 }{ 2 * sin 60° } = 29.44 ; ;




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