Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 336.07   b = 285   c = 507.51

Area: T = 45191.15222355
Perimeter: p = 1128.58
Semiperimeter: s = 564.29

Angle ∠ A = α = 38.67330974802° = 38°40'23″ = 0.6754972883 rad
Angle ∠ B = β = 321.9999466237° = 32° = 0.5598504429 rad
Angle ∠ C = γ = 109.3276955896° = 109°19'37″ = 1.90881153416 rad

Height: ha = 268.939892484
Height: hb = 317.1310892881
Height: hc = 178.0989701624

Median: ma = 375.713257475
Median: mb = 406.1388489311
Median: mc = 180.8110459944

Inradius: r = 80.08549779998
Circumradius: R = 268.9099288765

Vertex coordinates: A[507.51; 0] B[0; 0] C[285.0043689582; 178.0989701624]
Centroid: CG[264.1711229861; 59.36332338745]
Coordinates of the circumscribed circle: U[253.755; -88.99877840128]
Coordinates of the inscribed circle: I[279.29; 80.08549779998]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.327690252° = 141°19'37″ = 0.6754972883 rad
∠ B' = β' = 1488.000053376° = 148° = 0.5598504429 rad
∠ C' = γ' = 70.67330441039° = 70°40'23″ = 1.90881153416 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 = 336.07+285+507.51 = 1128.58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1128.58 }{ 2 } = 564.29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 564.29 * (564.29-336.07)(564.29-285)(564.29-507.51) } ; ; T = sqrt{ 2042240240.37 } = 45191.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 45191.15 }{ 336.07 } = 268.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 45191.15 }{ 285 } = 317.13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 45191.15 }{ 507.51 } = 178.09 ; ;

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{ 285**2+507.51**2-336.07**2 }{ 2 * 285 * 507.51 } ) = 38° 40'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 336.07**2+507.51**2-285**2 }{ 2 * 336.07 * 507.51 } ) = 32° ; ;
 gamma = 180° - alpha - beta = 180° - 38° 40'23" - 32° = 109° 19'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 45191.15 }{ 564.29 } = 80.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 336.07 }{ 2 * sin 38° 40'23" } = 268.91 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 285**2+2 * 507.51**2 - 336.07**2 } }{ 2 } = 375.713 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 507.51**2+2 * 336.07**2 - 285**2 } }{ 2 } = 406.138 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 285**2+2 * 336.07**2 - 507.51**2 } }{ 2 } = 180.81 ; ;
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