152 140 51 triangle

Obtuse scalene triangle.

Sides: a = 152   b = 140   c = 51

Area: T = 3562.855516651
Perimeter: p = 343
Semiperimeter: s = 171.5

Angle ∠ A = α = 93.62655344513° = 93°37'32″ = 1.63440738401 rad
Angle ∠ B = β = 66.81107563566° = 66°48'39″ = 1.16660676742 rad
Angle ∠ C = γ = 19.56437091922° = 19°33'49″ = 0.34114511393 rad

Height: ha = 46.88796732435
Height: hb = 50.89879309501
Height: hc = 139.7219810451

Median: ma = 72.96991715727
Median: mb = 89.17767907025
Median: mc = 143.8811027241

Inradius: r = 20.77546656939
Circumradius: R = 76.15224079201

Vertex coordinates: A[51; 0] B[0; 0] C[59.85329411765; 139.7219810451]
Centroid: CG[36.95109803922; 46.57332701504]
Coordinates of the circumscribed circle: U[25.5; 71.75661093708]
Coordinates of the inscribed circle: I[31.5; 20.77546656939]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 86.37444655487° = 86°22'28″ = 1.63440738401 rad
∠ B' = β' = 113.1899243643° = 113°11'21″ = 1.16660676742 rad
∠ C' = γ' = 160.4366290808° = 160°26'11″ = 0.34114511393 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 = 152+140+51 = 343 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 343 }{ 2 } = 171.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 171.5 * (171.5-152)(171.5-140)(171.5-51) } ; ; T = sqrt{ 12693936.94 } = 3562.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3562.86 }{ 152 } = 46.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3562.86 }{ 140 } = 50.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3562.86 }{ 51 } = 139.72 ; ;

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{ 140**2+51**2-152**2 }{ 2 * 140 * 51 } ) = 93° 37'32" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 152**2+51**2-140**2 }{ 2 * 152 * 51 } ) = 66° 48'39" ; ;
gamma = 180° - alpha - beta = 180° - 93° 37'32" - 66° 48'39" = 19° 33'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3562.86 }{ 171.5 } = 20.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 152 }{ 2 * sin 93° 37'32" } = 76.15 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 140**2+2 * 51**2 - 152**2 } }{ 2 } = 72.969 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 51**2+2 * 152**2 - 140**2 } }{ 2 } = 89.177 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 140**2+2 * 152**2 - 51**2 } }{ 2 } = 143.881 ; ;
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