Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 62   b = 54   c = 11.06

Area: T = 220.4643717095
Perimeter: p = 127.06
Semiperimeter: s = 63.53

Angle ∠ A = α = 132.4155310972° = 132°24'55″ = 2.31110831565 rad
Angle ∠ B = β = 40.01769210768° = 40°1'1″ = 0.69884270293 rad
Angle ∠ C = γ = 7.56877679514° = 7°34'4″ = 0.13220824678 rad

Height: ha = 7.11217328095
Height: hb = 8.16553228554
Height: hc = 39.86768566175

Median: ma = 23.62554481439
Median: mb = 35.41441468908
Median: mc = 57.87441660847

Inradius: r = 3.47702300818
Circumradius: R = 41.99897664885

Vertex coordinates: A[11.06; 0] B[0; 0] C[47.48329837251; 39.86768566175]
Centroid: CG[19.51443279084; 13.28989522058]
Coordinates of the circumscribed circle: U[5.53; 41.62440265924]
Coordinates of the inscribed circle: I[9.53; 3.47702300818]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 47.58546890283° = 47°35'5″ = 2.31110831565 rad
∠ B' = β' = 139.9833078923° = 139°58'59″ = 0.69884270293 rad
∠ C' = γ' = 172.4322232049° = 172°25'56″ = 0.13220824678 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 = 62+54+11.06 = 127.06 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 127.06 }{ 2 } = 63.53 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 63.53 * (63.53-62)(63.53-54)(63.53-11.06) } ; ; T = sqrt{ 48604.25 } = 220.46 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 220.46 }{ 62 } = 7.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 220.46 }{ 54 } = 8.17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 220.46 }{ 11.06 } = 39.87 ; ;

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{ 54**2+11.06**2-62**2 }{ 2 * 54 * 11.06 } ) = 132° 24'55" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 62**2+11.06**2-54**2 }{ 2 * 62 * 11.06 } ) = 40° 1'1" ; ; gamma = 180° - alpha - beta = 180° - 132° 24'55" - 40° 1'1" = 7° 34'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 220.46 }{ 63.53 } = 3.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 62 }{ 2 * sin 132° 24'55" } = 41.99 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 54**2+2 * 11.06**2 - 62**2 } }{ 2 } = 23.625 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.06**2+2 * 62**2 - 54**2 } }{ 2 } = 35.414 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 54**2+2 * 62**2 - 11.06**2 } }{ 2 } = 57.874 ; ;
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