Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 56.49   b = 25.3   c = 31.2

Area: T = 14.9329657527
Perimeter: p = 112.99
Semiperimeter: s = 56.495

Angle ∠ A = α = 177.8322141234° = 177°49'56″ = 3.10437563804 rad
Angle ∠ B = β = 0.97107269388° = 0°58'15″ = 0.01769423812 rad
Angle ∠ C = γ = 1.19771318267° = 1°11'50″ = 0.0210893892 rad

Height: ha = 0.52985770057
Height: hb = 1.18802100812
Height: hc = 0.95770293287

Median: ma = 2.99774947873
Median: mb = 43.84435576795
Median: mc = 40.89330929376

Inradius: r = 0.26442651124
Circumradius: R = 746.6844013335

Vertex coordinates: A[31.2; 0] B[0; 0] C[56.48218926282; 0.95770293287]
Centroid: CG[29.22772975427; 0.31990097762]
Coordinates of the circumscribed circle: U[15.6; 746.5211035048]
Coordinates of the inscribed circle: I[31.195; 0.26442651124]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 2.16878587655° = 2°10'4″ = 3.10437563804 rad
∠ B' = β' = 179.0299273061° = 179°1'45″ = 0.01769423812 rad
∠ C' = γ' = 178.8032868173° = 178°48'10″ = 0.0210893892 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 = 56.49+25.3+31.2 = 112.99 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 112.99 }{ 2 } = 56.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 56.5 * (56.5-56.49)(56.5-25.3)(56.5-31.2) } ; ; T = sqrt{ 222.89 } = 14.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14.93 }{ 56.49 } = 0.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14.93 }{ 25.3 } = 1.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14.93 }{ 31.2 } = 0.96 ; ;

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{ 25.3**2+31.2**2-56.49**2 }{ 2 * 25.3 * 31.2 } ) = 177° 49'56" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 56.49**2+31.2**2-25.3**2 }{ 2 * 56.49 * 31.2 } ) = 0° 58'15" ; ;
 gamma = 180° - alpha - beta = 180° - 177° 49'56" - 0° 58'15" = 1° 11'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14.93 }{ 56.5 } = 0.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 56.49 }{ 2 * sin 177° 49'56" } = 746.68 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 25.3**2+2 * 31.2**2 - 56.49**2 } }{ 2 } = 2.997 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 31.2**2+2 * 56.49**2 - 25.3**2 } }{ 2 } = 43.844 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 25.3**2+2 * 56.49**2 - 31.2**2 } }{ 2 } = 40.893 ; ;
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