Triangle calculator SSS - result

Please enter the triangle sides:


Equilateral triangle.

Sides: a = 11.55   b = 11.55   c = 11.55

Area: T = 57.76549769642
Perimeter: p = 34.65
Semiperimeter: s = 17.325

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

Height: ha = 10.00325934137
Height: hb = 10.00325934137
Height: hc = 10.00325934137

Median: ma = 10.00325934137
Median: mb = 10.00325934137
Median: mc = 10.00325934137

Inradius: r = 3.33441978046
Circumradius: R = 6.66883956091

Vertex coordinates: A[11.55; 0] B[0; 0] C[5.775; 10.00325934137]
Centroid: CG[5.775; 3.33441978046]
Coordinates of the circumscribed circle: U[5.775; 3.33441978046]
Coordinates of the inscribed circle: I[5.775; 3.33441978046]

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?

a = 11.55 ; ; b = 11.55 ; ; c = 11.55 ; ;

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

p = a+b+c = 11.55+11.55+11.55 = 34.65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34.65 }{ 2 } = 17.33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.33 * (17.33-11.55)(17.33-11.55)(17.33-11.55) } ; ; T = sqrt{ 3336.79 } = 57.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 57.76 }{ 11.55 } = 10 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 57.76 }{ 11.55 } = 10 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 57.76 }{ 11.55 } = 10 ; ;

5. 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{ 11.55**2-11.55**2-11.55**2 }{ 2 * 11.55 * 11.55 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11.55**2-11.55**2-11.55**2 }{ 2 * 11.55 * 11.55 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11.55**2-11.55**2-11.55**2 }{ 2 * 11.55 * 11.55 } ) = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 57.76 }{ 17.33 } = 3.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11.55 }{ 2 * sin 60° } = 6.67 ; ;




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