Triangle calculator SSS - result

Please enter the triangle sides:


Equilateral triangle.

Sides: a = 17.32   b = 17.32   c = 17.32

Area: T = 129.8966189544
Perimeter: p = 51.96
Semiperimeter: s = 25.98

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

Height: ha = 154.9995599935
Height: hb = 154.9995599935
Height: hc = 154.9995599935

Median: ma = 154.9995599935
Median: mb = 154.9995599935
Median: mc = 154.9995599935

Inradius: r = 54.9998533312
Circumradius: R = 10.9997066624

Vertex coordinates: A[17.32; 0] B[0; 0] C[8.66; 154.9995599935]
Centroid: CG[8.66; 54.9998533312]
Coordinates of the circumscribed circle: U[8.66; 54.9998533312]
Coordinates of the inscribed circle: I[8.66; 54.9998533312]

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 = 17.32+17.32+17.32 = 51.96 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51.96 }{ 2 } = 25.98 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.98 * (25.98-17.32)(25.98-17.32)(25.98-17.32) } ; ; T = sqrt{ 16873.02 } = 129.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 129.9 }{ 17.32 } = 15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 129.9 }{ 17.32 } = 15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 129.9 }{ 17.32 } = 15 ; ;

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{ 17.32**2+17.32**2-17.32**2 }{ 2 * 17.32 * 17.32 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 17.32**2+17.32**2-17.32**2 }{ 2 * 17.32 * 17.32 } ) = 60° ; ; gamma = 180° - alpha - beta = 180° - 60° - 60° = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 129.9 }{ 25.98 } = 5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 17.32 }{ 2 * sin 60° } = 10 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 17.32**2+2 * 17.32**2 - 17.32**2 } }{ 2 } = 15 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 17.32**2+2 * 17.32**2 - 17.32**2 } }{ 2 } = 15 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 17.32**2+2 * 17.32**2 - 17.32**2 } }{ 2 } = 15 ; ;
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