Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 149   b = 176   c = 318.56

Area: T = 5108.615491854
Perimeter: p = 643.56
Semiperimeter: s = 321.78

Angle ∠ A = α = 10.54999073054° = 10°30' = 0.18332579536 rad
Angle ∠ B = β = 12.43105579196° = 12°25'50″ = 0.21769541636 rad
Angle ∠ C = γ = 157.0769534775° = 157°4'10″ = 2.74113805364 rad

Height: ha = 68.57220123293
Height: hb = 58.05224422561
Height: hc = 32.07331725172

Median: ma = 246.3299021433
Median: mb = 232.587705209
Median: mc = 34.90553233762

Inradius: r = 15.87661107544
Circumradius: R = 408.8155186367

Vertex coordinates: A[318.56; 0] B[0; 0] C[145.507708438; 32.07331725172]
Centroid: CG[154.6899028127; 10.69110575057]
Coordinates of the circumscribed circle: U[159.28; -376.5109944363]
Coordinates of the inscribed circle: I[145.78; 15.87661107544]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.5500092695° = 169°30' = 0.18332579536 rad
∠ B' = β' = 167.569944208° = 167°34'10″ = 0.21769541636 rad
∠ C' = γ' = 22.9330465225° = 22°55'50″ = 2.74113805364 rad

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How did we calculate this triangle?

a = 149 ; ; b = 176 ; ; c = 318.56 ; ;

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

p = a+b+c = 149+176+318.56 = 643.56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 643.56 }{ 2 } = 321.78 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 321.78 * (321.78-149)(321.78-176)(321.78-318.56) } ; ; T = sqrt{ 26097946.39 } = 5108.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5108.61 }{ 149 } = 68.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5108.61 }{ 176 } = 58.05 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5108.61 }{ 318.56 } = 32.07 ; ;

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{ 176**2+318.56**2-149**2 }{ 2 * 176 * 318.56 } ) = 10° 30' ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 149**2+318.56**2-176**2 }{ 2 * 149 * 318.56 } ) = 12° 25'50" ; ; gamma = 180° - alpha - beta = 180° - 10° 30' - 12° 25'50" = 157° 4'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5108.61 }{ 321.78 } = 15.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 149 }{ 2 * sin 10° 30' } = 408.82 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 176**2+2 * 318.56**2 - 149**2 } }{ 2 } = 246.329 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 318.56**2+2 * 149**2 - 176**2 } }{ 2 } = 232.587 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 176**2+2 * 149**2 - 318.56**2 } }{ 2 } = 34.905 ; ;
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