Triangle calculator SSS - result

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Obtuse scalene triangle.

Sides: a = 119   b = 70   c = 66.18

Area: T = 1968.78436252
Perimeter: p = 255.18
Semiperimeter: s = 127.59

Angle ∠ A = α = 121.7921681974° = 121°47'30″ = 2.1265665852 rad
Angle ∠ B = β = 29.9998800803° = 29°59'56″ = 0.52435778457 rad
Angle ∠ C = γ = 28.21095172226° = 28°12'34″ = 0.49223489559 rad

Height: ha = 33.08988004235
Height: hb = 56.251096072
Height: hc = 59.498784301

Median: ma = 33.16109137389
Median: mb = 89.69661325811
Median: mc = 91.8455260629

Inradius: r = 15.43105480461
Circumradius: R = 70.00325377273

Vertex coordinates: A[66.18; 0] B[0; 0] C[103.0588268359; 59.498784301]
Centroid: CG[56.41327561197; 19.83326143367]
Coordinates of the circumscribed circle: U[33.09; 61.68879825271]
Coordinates of the inscribed circle: I[57.59; 15.43105480461]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 58.20883180256° = 58°12'30″ = 2.1265665852 rad
∠ B' = β' = 150.0011199197° = 150°4″ = 0.52435778457 rad
∠ C' = γ' = 151.7990482777° = 151°47'26″ = 0.49223489559 rad

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How did we calculate this triangle?

a = 119 ; ; b = 70 ; ; c = 66.18 ; ;

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

p = a+b+c = 119+70+66.18 = 255.18 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 255.18 }{ 2 } = 127.59 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 127.59 * (127.59-119)(127.59-70)(127.59-66.18) } ; ; T = sqrt{ 3876108.96 } = 1968.78 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1968.78 }{ 119 } = 33.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1968.78 }{ 70 } = 56.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1968.78 }{ 66.18 } = 59.5 ; ;

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{ 70**2+66.18**2-119**2 }{ 2 * 70 * 66.18 } ) = 121° 47'30" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 119**2+66.18**2-70**2 }{ 2 * 119 * 66.18 } ) = 29° 59'56" ; ; gamma = 180° - alpha - beta = 180° - 121° 47'30" - 29° 59'56" = 28° 12'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1968.78 }{ 127.59 } = 15.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 119 }{ 2 * sin 121° 47'30" } = 70 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 70**2+2 * 66.18**2 - 119**2 } }{ 2 } = 33.161 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 66.18**2+2 * 119**2 - 70**2 } }{ 2 } = 89.696 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 70**2+2 * 119**2 - 66.18**2 } }{ 2 } = 91.845 ; ;
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