Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 107   b = 77   c = 152.83

Area: T = 3838.749928015
Perimeter: p = 336.83
Semiperimeter: s = 168.415

Angle ∠ A = α = 40.72435298078° = 40°43'25″ = 0.71107596782 rad
Angle ∠ B = β = 28.00112670337° = 28°5″ = 0.48987143045 rad
Angle ∠ C = γ = 111.2755203159° = 111°16'31″ = 1.94221186709 rad

Height: ha = 71.75223229935
Height: hb = 99.70877735104
Height: hc = 50.23655464261

Median: ma = 108.5399183938
Median: mb = 126.1777472038
Median: mc = 53.38330289043

Inradius: r = 22.79333929885
Circumradius: R = 82.00436864944

Vertex coordinates: A[152.83; 0] B[0; 0] C[94.47442815547; 50.23655464261]
Centroid: CG[82.43547605182; 16.7455182142]
Coordinates of the circumscribed circle: U[76.415; -29.75548714275]
Coordinates of the inscribed circle: I[91.415; 22.79333929885]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.2766470192° = 139°16'35″ = 0.71107596782 rad
∠ B' = β' = 151.9998732966° = 151°59'55″ = 0.48987143045 rad
∠ C' = γ' = 68.72547968415° = 68°43'29″ = 1.94221186709 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 = 107+77+152.83 = 336.83 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 336.83 }{ 2 } = 168.42 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 168.42 * (168.42-107)(168.42-77)(168.42-152.83) } ; ; T = sqrt{ 14735996.04 } = 3838.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3838.75 }{ 107 } = 71.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3838.75 }{ 77 } = 99.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3838.75 }{ 152.83 } = 50.24 ; ;

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{ 77**2+152.83**2-107**2 }{ 2 * 77 * 152.83 } ) = 40° 43'25" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 107**2+152.83**2-77**2 }{ 2 * 107 * 152.83 } ) = 28° 5" ; ;
 gamma = 180° - alpha - beta = 180° - 40° 43'25" - 28° 5" = 111° 16'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3838.75 }{ 168.42 } = 22.79 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 107 }{ 2 * sin 40° 43'25" } = 82 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 77**2+2 * 152.83**2 - 107**2 } }{ 2 } = 108.539 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 152.83**2+2 * 107**2 - 77**2 } }{ 2 } = 126.177 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 77**2+2 * 107**2 - 152.83**2 } }{ 2 } = 53.383 ; ;
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