Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 12.65   b = 14.14   c = 6.32

Area: T = 39.97439994996
Perimeter: p = 33.11
Semiperimeter: s = 16.555

Angle ∠ A = α = 63.46603240254° = 63°27'37″ = 1.10875915986 rad
Angle ∠ B = β = 89.99109342121° = 89°59'27″ = 1.57106380989 rad
Angle ∠ C = γ = 26.54987417625° = 26°32'55″ = 0.4633362956 rad

Height: ha = 6.32199999209
Height: hb = 5.65440310466
Height: hc = 12.65499998416

Median: ma = 8.94106585328
Median: mb = 7.07108945686
Median: mc = 13.03882303247

Inradius: r = 2.415461791
Circumradius: R = 7.07700000885

Vertex coordinates: A[6.32; 0] B[0; 0] C[0.00220015823; 12.65499998416]
Centroid: CG[2.10773338608; 4.21766666139]
Coordinates of the circumscribed circle: U[3.16; 6.32545000792]
Coordinates of the inscribed circle: I[2.415; 2.415461791]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.5439675975° = 116°32'23″ = 1.10875915986 rad
∠ B' = β' = 90.00990657879° = 90°33″ = 1.57106380989 rad
∠ C' = γ' = 153.4511258237° = 153°27'5″ = 0.4633362956 rad

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How did we calculate this triangle?

a = 12.65 ; ; b = 14.14 ; ; c = 6.32 ; ;

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

p = a+b+c = 12.65+14.14+6.32 = 33.11 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33.11 }{ 2 } = 16.56 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.56 * (16.56-12.65)(16.56-14.14)(16.56-6.32) } ; ; T = sqrt{ 1597.92 } = 39.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 39.97 }{ 12.65 } = 6.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 39.97 }{ 14.14 } = 5.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 39.97 }{ 6.32 } = 12.65 ; ;

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{ 14.14**2+6.32**2-12.65**2 }{ 2 * 14.14 * 6.32 } ) = 63° 27'37" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 12.65**2+6.32**2-14.14**2 }{ 2 * 12.65 * 6.32 } ) = 89° 59'27" ; ; gamma = 180° - alpha - beta = 180° - 63° 27'37" - 89° 59'27" = 26° 32'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 39.97 }{ 16.56 } = 2.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 12.65 }{ 2 * sin 63° 27'37" } = 7.07 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.14**2+2 * 6.32**2 - 12.65**2 } }{ 2 } = 8.941 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.32**2+2 * 12.65**2 - 14.14**2 } }{ 2 } = 7.071 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.14**2+2 * 12.65**2 - 6.32**2 } }{ 2 } = 13.038 ; ;
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