Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 46   b = 42   c = 4.69

Area: T = 53.79546951293
Perimeter: p = 92.69
Semiperimeter: s = 46.345

Angle ∠ A = α = 146.8943671384° = 146°53'37″ = 2.5643778216 rad
Angle ∠ B = β = 29.914398463° = 29°54'50″ = 0.52220975242 rad
Angle ∠ C = γ = 3.19223439862° = 3°11'32″ = 0.05657169134 rad

Height: ha = 2.33988997882
Height: hb = 2.5621652149
Height: hc = 22.94401684986

Median: ma = 19.07987329244
Median: mb = 25.06598892655
Median: mc = 43.98329623263

Inradius: r = 1.16107443118
Circumradius: R = 42.11095424848

Vertex coordinates: A[4.69; 0] B[0; 0] C[39.8721652452; 22.94401684986]
Centroid: CG[14.85438841507; 7.64767228329]
Coordinates of the circumscribed circle: U[2.345; 42.04441974983]
Coordinates of the inscribed circle: I[4.345; 1.16107443118]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 33.10663286162° = 33°6'23″ = 2.5643778216 rad
∠ B' = β' = 150.086601537° = 150°5'10″ = 0.52220975242 rad
∠ C' = γ' = 176.8087656014° = 176°48'28″ = 0.05657169134 rad

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How did we calculate this triangle?

a = 46 ; ; b = 42 ; ; c = 4.69 ; ;

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

p = a+b+c = 46+42+4.69 = 92.69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 92.69 }{ 2 } = 46.35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 46.35 * (46.35-46)(46.35-42)(46.35-4.69) } ; ; T = sqrt{ 2893.87 } = 53.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 53.79 }{ 46 } = 2.34 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 53.79 }{ 42 } = 2.56 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 53.79 }{ 4.69 } = 22.94 ; ;

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{ 42**2+4.69**2-46**2 }{ 2 * 42 * 4.69 } ) = 146° 53'37" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 46**2+4.69**2-42**2 }{ 2 * 46 * 4.69 } ) = 29° 54'50" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 46**2+42**2-4.69**2 }{ 2 * 46 * 42 } ) = 3° 11'32" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 53.79 }{ 46.35 } = 1.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 46 }{ 2 * sin 146° 53'37" } = 42.11 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 42**2+2 * 4.69**2 - 46**2 } }{ 2 } = 19.079 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.69**2+2 * 46**2 - 42**2 } }{ 2 } = 25.06 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 42**2+2 * 46**2 - 4.69**2 } }{ 2 } = 43.983 ; ;
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