Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 336.07   b = 285   c = 62.49

Area: T = 5563.099868376
Perimeter: p = 683.56
Semiperimeter: s = 341.78

Angle ∠ A = α = 141.3387731228° = 141°20'16″ = 2.46768087672 rad
Angle ∠ B = β = 31.9911492252° = 31°59'29″ = 0.55883568724 rad
Angle ∠ C = γ = 6.67107765198° = 6°40'15″ = 0.11664270139 rad

Height: ha = 33.10767853944
Height: hb = 39.03992890088
Height: hc = 178.0487645503

Median: ma = 119.7054798672
Median: mb = 195.2387733289
Median: mc = 310.0132535916

Inradius: r = 16.27768409028
Circumradius: R = 268.9732807052

Vertex coordinates: A[62.49; 0] B[0; 0] C[285.0329964794; 178.0487645503]
Centroid: CG[115.8439988265; 59.34992151678]
Coordinates of the circumscribed circle: U[31.245; 267.1521868622]
Coordinates of the inscribed circle: I[56.78; 16.27768409028]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 38.66222687718° = 38°39'44″ = 2.46768087672 rad
∠ B' = β' = 148.0098507748° = 148°31″ = 0.55883568724 rad
∠ C' = γ' = 173.329922348° = 173°19'45″ = 0.11664270139 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 = 336.07+285+62.49 = 683.56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 683.56 }{ 2 } = 341.78 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 341.78 * (341.78-336.07)(341.78-285)(341.78-62.49) } ; ; T = sqrt{ 30948066.97 } = 5563.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5563.1 }{ 336.07 } = 33.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5563.1 }{ 285 } = 39.04 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5563.1 }{ 62.49 } = 178.05 ; ;

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{ 285**2+62.49**2-336.07**2 }{ 2 * 285 * 62.49 } ) = 141° 20'16" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 336.07**2+62.49**2-285**2 }{ 2 * 336.07 * 62.49 } ) = 31° 59'29" ; ;
 gamma = 180° - alpha - beta = 180° - 141° 20'16" - 31° 59'29" = 6° 40'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5563.1 }{ 341.78 } = 16.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 336.07 }{ 2 * sin 141° 20'16" } = 268.97 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 285**2+2 * 62.49**2 - 336.07**2 } }{ 2 } = 119.705 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 62.49**2+2 * 336.07**2 - 285**2 } }{ 2 } = 195.238 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 285**2+2 * 336.07**2 - 62.49**2 } }{ 2 } = 310.013 ; ;
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