Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 60   b = 50   c = 12.29

Area: T = 195.2444029975
Perimeter: p = 122.29
Semiperimeter: s = 61.145

Angle ∠ A = α = 140.5466144638° = 140°32'46″ = 2.45329929749 rad
Angle ∠ B = β = 31.97548619083° = 31°58'29″ = 0.55880666182 rad
Angle ∠ C = γ = 7.47989934533° = 7°28'44″ = 0.13105330605 rad

Height: ha = 6.50881343325
Height: hb = 7.8109761199
Height: hc = 31.77328283117

Median: ma = 20.62881858146
Median: mb = 35.36327211905
Median: mc = 54.88438680761

Inradius: r = 3.19331315721
Circumradius: R = 47.21101502984

Vertex coordinates: A[12.29; 0] B[0; 0] C[50.89768307567; 31.77328283117]
Centroid: CG[21.06222769189; 10.59109427706]
Coordinates of the circumscribed circle: U[6.145; 46.80985170263]
Coordinates of the inscribed circle: I[11.145; 3.19331315721]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 39.45438553616° = 39°27'14″ = 2.45329929749 rad
∠ B' = β' = 148.0255138092° = 148°1'31″ = 0.55880666182 rad
∠ C' = γ' = 172.5211006547° = 172°31'16″ = 0.13105330605 rad

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How did we calculate this triangle?

a = 60 ; ; b = 50 ; ; c = 12.29 ; ;

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

p = a+b+c = 60+50+12.29 = 122.29 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 122.29 }{ 2 } = 61.15 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 61.15 * (61.15-60)(61.15-50)(61.15-12.29) } ; ; T = sqrt{ 38120.23 } = 195.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 195.24 }{ 60 } = 6.51 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 195.24 }{ 50 } = 7.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 195.24 }{ 12.29 } = 31.77 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 60**2-50**2-12.29**2 }{ 2 * 50 * 12.29 } ) = 140° 32'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 50**2-60**2-12.29**2 }{ 2 * 60 * 12.29 } ) = 31° 58'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12.29**2-60**2-50**2 }{ 2 * 50 * 60 } ) = 7° 28'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 195.24 }{ 61.15 } = 3.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 60 }{ 2 * sin 140° 32'46" } = 47.21 ; ;




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