Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 120.32   b = 204.61   c = 179.95

Area: T = 10753.56985663
Perimeter: p = 504.88
Semiperimeter: s = 252.44

Angle ∠ A = α = 35.74110192707° = 35°44'28″ = 0.62437984643 rad
Angle ∠ B = β = 83.37880087917° = 83°22'41″ = 1.45552207772 rad
Angle ∠ C = γ = 60.88109719376° = 60°52'51″ = 1.06325734121 rad

Height: ha = 178.7499477498
Height: hb = 105.113283482
Height: hc = 119.5177294429

Median: ma = 183.042207631
Median: mb = 113.856578345
Median: mc = 141.6888308004

Inradius: r = 42.59985127803
Circumradius: R = 102.9922103852

Vertex coordinates: A[179.95; 0] B[0; 0] C[13.87551119755; 119.5177294429]
Centroid: CG[64.60883706585; 39.83990981431]
Coordinates of the circumscribed circle: U[89.975; 50.1198587679]
Coordinates of the inscribed circle: I[47.83; 42.59985127803]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.2598980729° = 144°15'32″ = 0.62437984643 rad
∠ B' = β' = 96.62219912083° = 96°37'19″ = 1.45552207772 rad
∠ C' = γ' = 119.1199028062° = 119°7'9″ = 1.06325734121 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 = 120.32+204.61+179.95 = 504.88 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 504.88 }{ 2 } = 252.44 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 252.44 * (252.44-120.32)(252.44-204.61)(252.44-179.95) } ; ; T = sqrt{ 115639236.91 } = 10753.57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10753.57 }{ 120.32 } = 178.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10753.57 }{ 204.61 } = 105.11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10753.57 }{ 179.95 } = 119.52 ; ;

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{ 204.61**2+179.95**2-120.32**2 }{ 2 * 204.61 * 179.95 } ) = 35° 44'28" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 120.32**2+179.95**2-204.61**2 }{ 2 * 120.32 * 179.95 } ) = 83° 22'41" ; ; gamma = 180° - alpha - beta = 180° - 35° 44'28" - 83° 22'41" = 60° 52'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10753.57 }{ 252.44 } = 42.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 120.32 }{ 2 * sin 35° 44'28" } = 102.99 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 204.61**2+2 * 179.95**2 - 120.32**2 } }{ 2 } = 183.042 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 179.95**2+2 * 120.32**2 - 204.61**2 } }{ 2 } = 113.856 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 204.61**2+2 * 120.32**2 - 179.95**2 } }{ 2 } = 141.688 ; ;
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