Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 50   b = 60   c = 14.14

Area: T = 272.6366121547
Perimeter: p = 124.14
Semiperimeter: s = 62.07

Angle ∠ A = α = 39.99439379997° = 39°59'38″ = 0.69880258989 rad
Angle ∠ B = β = 129.5343921019° = 129°32'2″ = 2.26107934148 rad
Angle ∠ C = γ = 10.47221409816° = 10°28'20″ = 0.18327733399 rad

Height: ha = 10.90554448619
Height: hb = 9.08878707182
Height: hc = 38.56223934295

Median: ma = 35.70767192556
Median: mb = 21.21224916028
Median: mc = 54.77223935939

Inradius: r = 4.39223976405
Circumradius: R = 38.89880005285

Vertex coordinates: A[14.14; 0] B[0; 0] C[-31.82767468175; 38.56223934295]
Centroid: CG[-5.89655822725; 12.85441311432]
Coordinates of the circumscribed circle: U[7.07; 38.25500920929]
Coordinates of the inscribed circle: I[2.07; 4.39223976405]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.0066062° = 140°22″ = 0.69880258989 rad
∠ B' = β' = 50.46660789813° = 50°27'58″ = 2.26107934148 rad
∠ C' = γ' = 169.5287859018° = 169°31'40″ = 0.18327733399 rad

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How did we calculate this triangle?

a = 50 ; ; b = 60 ; ; c = 14.14 ; ;

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

p = a+b+c = 50+60+14.14 = 124.14 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 124.14 }{ 2 } = 62.07 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 62.07 * (62.07-50)(62.07-60)(62.07-14.14) } ; ; T = sqrt{ 74330.45 } = 272.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 272.64 }{ 50 } = 10.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 272.64 }{ 60 } = 9.09 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 272.64 }{ 14.14 } = 38.56 ; ;

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+14.14**2-50**2 }{ 2 * 60 * 14.14 } ) = 39° 59'38" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 50**2+14.14**2-60**2 }{ 2 * 50 * 14.14 } ) = 129° 32'2" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 50**2+60**2-14.14**2 }{ 2 * 50 * 60 } ) = 10° 28'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 272.64 }{ 62.07 } = 4.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 50 }{ 2 * sin 39° 59'38" } = 38.9 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 14.14**2 - 50**2 } }{ 2 } = 35.707 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.14**2+2 * 50**2 - 60**2 } }{ 2 } = 21.212 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 50**2 - 14.14**2 } }{ 2 } = 54.772 ; ;
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