Triangle calculator SSS - result

Please enter the triangle sides:


Equilateral triangle.

Sides: a = 13.51   b = 13.51   c = 13.51

Area: T = 79.03435216506
Perimeter: p = 40.53
Semiperimeter: s = 20.265

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

Height: ha = 11.77000032051
Height: hb = 11.77000032051
Height: hc = 11.77000032051

Median: ma = 11.77000032051
Median: mb = 11.77000032051
Median: mc = 11.77000032051

Inradius: r = 3.99000010684
Circumradius: R = 7.88000021368

Vertex coordinates: A[13.51; 0] B[0; 0] C[6.755; 11.77000032051]
Centroid: CG[6.755; 3.99000010684]
Coordinates of the circumscribed circle: U[6.755; 3.99000010684]
Coordinates of the inscribed circle: I[6.755; 3.99000010684]

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

p = a+b+c = 13.51+13.51+13.51 = 40.53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40.53 }{ 2 } = 20.27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.27 * (20.27-13.51)(20.27-13.51)(20.27-13.51) } ; ; T = sqrt{ 6246.3 } = 79.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 79.03 }{ 13.51 } = 11.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 79.03 }{ 13.51 } = 11.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 79.03 }{ 13.51 } = 11.7 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 13.51**2+13.51**2-13.51**2 }{ 2 * 13.51 * 13.51 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 13.51**2+13.51**2-13.51**2 }{ 2 * 13.51 * 13.51 } ) = 60° ; ; gamma = 180° - alpha - beta = 180° - 60° - 60° = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 79.03 }{ 20.27 } = 3.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 13.51 }{ 2 * sin 60° } = 7.8 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.51**2+2 * 13.51**2 - 13.51**2 } }{ 2 } = 11.7 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.51**2+2 * 13.51**2 - 13.51**2 } }{ 2 } = 11.7 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.51**2+2 * 13.51**2 - 13.51**2 } }{ 2 } = 11.7 ; ;
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