Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 102   b = 60   c = 56.73

Area: T = 1446.687987028
Perimeter: p = 218.73
Semiperimeter: s = 109.365

Angle ∠ A = α = 121.7844184627° = 121°47'3″ = 2.12655349986 rad
Angle ∠ B = β = 30.00114833992° = 30°5″ = 0.52436246658 rad
Angle ∠ C = γ = 28.21443319733° = 28°12'52″ = 0.49224329892 rad

Height: ha = 28.36662719662
Height: hb = 48.22326623425
Height: hc = 51.00222869831

Median: ma = 28.42879167369
Median: mb = 76.88439804511
Median: mc = 78.72437370493

Inradius: r = 13.22879968022
Circumradius: R = 59.99773095523

Vertex coordinates: A[56.73; 0] B[0; 0] C[88.33332707562; 51.00222869831]
Centroid: CG[48.35444235854; 17.00107623277]
Coordinates of the circumscribed circle: U[28.365; 52.86987424525]
Coordinates of the inscribed circle: I[49.365; 13.22879968022]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 58.21658153725° = 58°12'57″ = 2.12655349986 rad
∠ B' = β' = 149.9998516601° = 149°59'55″ = 0.52436246658 rad
∠ C' = γ' = 151.7865668027° = 151°47'8″ = 0.49224329892 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 = 102+60+56.73 = 218.73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 218.73 }{ 2 } = 109.37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 109.37 * (109.37-102)(109.37-60)(109.37-56.73) } ; ; T = sqrt{ 2092882.65 } = 1446.68 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1446.68 }{ 102 } = 28.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1446.68 }{ 60 } = 48.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1446.68 }{ 56.73 } = 51 ; ;

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{ 60**2+56.73**2-102**2 }{ 2 * 60 * 56.73 } ) = 121° 47'3" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 102**2+56.73**2-60**2 }{ 2 * 102 * 56.73 } ) = 30° 5" ; ; gamma = 180° - alpha - beta = 180° - 121° 47'3" - 30° 5" = 28° 12'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1446.68 }{ 109.37 } = 13.23 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 102 }{ 2 * sin 121° 47'3" } = 60 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 56.73**2 - 102**2 } }{ 2 } = 28.428 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 56.73**2+2 * 102**2 - 60**2 } }{ 2 } = 76.884 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 102**2 - 56.73**2 } }{ 2 } = 78.724 ; ;
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