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

Calculate another triangle


How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 152 ; ; b = 140 ; ; c = 51 ; ;

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 ; ;
Calculate another triangle


Look also our friend's collection of math examples and problems:

See more information about triangles or more details on solving triangles.