Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 8.19   b = 7.21   c = 5.2

Area: T = 18.50664947248
Perimeter: p = 20.6
Semiperimeter: s = 10.3

Angle ∠ A = α = 80.8311372185° = 80°49'53″ = 1.41107735835 rad
Angle ∠ B = β = 60.35435651097° = 60°21'13″ = 1.05333684265 rad
Angle ∠ C = γ = 38.81550627052° = 38°48'54″ = 0.67774506436 rad

Height: ha = 4.51992905311
Height: hb = 5.13435630305
Height: hc = 7.11878825865

Median: ma = 4.76989647724
Median: mb = 5.83662680713
Median: mc = 7.26443031324

Inradius: r = 1.79767470607
Circumradius: R = 4.14879962111

Vertex coordinates: A[5.2; 0] B[0; 0] C[4.05111538462; 7.11878825865]
Centroid: CG[3.08437179487; 2.37326275288]
Coordinates of the circumscribed circle: U[2.6; 3.23220075135]
Coordinates of the inscribed circle: I[3.09; 1.79767470607]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 99.1698627815° = 99°10'7″ = 1.41107735835 rad
∠ B' = β' = 119.646643489° = 119°38'47″ = 1.05333684265 rad
∠ C' = γ' = 141.1854937295° = 141°11'6″ = 0.67774506436 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 = 8.19+7.21+5.2 = 20.6 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 20.6 }{ 2 } = 10.3 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.3 * (10.3-8.19)(10.3-7.21)(10.3-5.2) } ; ; T = sqrt{ 342.49 } = 18.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18.51 }{ 8.19 } = 4.52 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18.51 }{ 7.21 } = 5.13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18.51 }{ 5.2 } = 7.12 ; ;

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{ 7.21**2+5.2**2-8.19**2 }{ 2 * 7.21 * 5.2 } ) = 80° 49'53" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8.19**2+5.2**2-7.21**2 }{ 2 * 8.19 * 5.2 } ) = 60° 21'13" ; ; gamma = 180° - alpha - beta = 180° - 80° 49'53" - 60° 21'13" = 38° 48'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18.51 }{ 10.3 } = 1.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8.19 }{ 2 * sin 80° 49'53" } = 4.15 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.21**2+2 * 5.2**2 - 8.19**2 } }{ 2 } = 4.769 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.2**2+2 * 8.19**2 - 7.21**2 } }{ 2 } = 5.836 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.21**2+2 * 8.19**2 - 5.2**2 } }{ 2 } = 7.264 ; ;
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