Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 11.4   b = 9.49   c = 6.32

Area: T = 29.98883981178
Perimeter: p = 27.21
Semiperimeter: s = 13.605

Angle ∠ A = α = 89.9879699895° = 89°58'47″ = 1.57704420231 rad
Angle ∠ B = β = 56.35218705207° = 56°21'7″ = 0.98435256802 rad
Angle ∠ C = γ = 33.66884295843° = 33°40'6″ = 0.58876249502 rad

Height: ha = 5.26111224768
Height: hb = 6.32199996033
Height: hc = 9.49899994044

Median: ma = 5.70218637304
Median: mb = 7.90216564719
Median: mc = 10.00112224253

Inradius: r = 2.20442188988
Circumradius: R = 5.77000003578

Vertex coordinates: A[6.32; 0] B[0; 0] C[6.31766376582; 9.49899994044]
Centroid: CG[4.21222125527; 3.16333331348]
Coordinates of the circumscribed circle: U[3.16; 4.74438806982]
Coordinates of the inscribed circle: I[4.115; 2.20442188988]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90.0220300105° = 90°1'13″ = 1.57704420231 rad
∠ B' = β' = 123.6488129479° = 123°38'53″ = 0.98435256802 rad
∠ C' = γ' = 146.3321570416° = 146°19'54″ = 0.58876249502 rad

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How did we calculate this triangle?

a = 11.4 ; ; b = 9.49 ; ; c = 6.32 ; ;

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

p = a+b+c = 11.4+9.49+6.32 = 27.21 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27.21 }{ 2 } = 13.61 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.61 * (13.61-11.4)(13.61-9.49)(13.61-6.32) } ; ; T = sqrt{ 899.3 } = 29.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.99 }{ 11.4 } = 5.26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.99 }{ 9.49 } = 6.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.99 }{ 6.32 } = 9.49 ; ;

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{ 9.49**2+6.32**2-11.4**2 }{ 2 * 9.49 * 6.32 } ) = 89° 58'47" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 11.4**2+6.32**2-9.49**2 }{ 2 * 11.4 * 6.32 } ) = 56° 21'7" ; ; gamma = 180° - alpha - beta = 180° - 89° 58'47" - 56° 21'7" = 33° 40'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.99 }{ 13.61 } = 2.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 11.4 }{ 2 * sin 89° 58'47" } = 5.7 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.49**2+2 * 6.32**2 - 11.4**2 } }{ 2 } = 5.702 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.32**2+2 * 11.4**2 - 9.49**2 } }{ 2 } = 7.902 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.49**2+2 * 11.4**2 - 6.32**2 } }{ 2 } = 10.001 ; ;
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