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 = 81   b = 81   c = 81

Area: T = 2840.996633711
Perimeter: p = 243
Semiperimeter: s = 121.5

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

Height: ha = 70.14880577065
Height: hb = 70.14880577065
Height: hc = 70.14880577065

Median: ma = 70.14880577065
Median: mb = 70.14880577065
Median: mc = 70.14880577065

Inradius: r = 23.38326859022
Circumradius: R = 46.76553718044

Vertex coordinates: A[81; 0] B[0; 0] C[40.5; 70.14880577065]
Centroid: CG[40.5; 23.38326859022]
Coordinates of the circumscribed circle: U[40.5; 23.38326859022]
Coordinates of the inscribed circle: I[40.5; 23.38326859022]

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 = 81 ; ; b = 81 ; ; c = 81 ; ;


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 = 81 ; ; b = 81 ; ; c = 81 ; ; : Nr. 1

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

p = a+b+c = 81+81+81 = 243 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 243 }{ 2 } = 121.5 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 121.5 * (121.5-81)(121.5-81)(121.5-81) } ; ; T = sqrt{ 8071260.19 } = 2841 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2841 }{ 81 } = 70.15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2841 }{ 81 } = 70.15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2841 }{ 81 } = 70.15 ; ;

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{ 81**2-81**2-81**2 }{ 2 * 81 * 81 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 81**2-81**2-81**2 }{ 2 * 81 * 81 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 81**2-81**2-81**2 }{ 2 * 81 * 81 } ) = 60° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2841 }{ 121.5 } = 23.38 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 81 }{ 2 * sin 60° } = 46.77 ; ;




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