6 23 27 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 23   c = 27

Area: T = 55.4987747702
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 10.29661852424° = 10°17'46″ = 0.18797023329 rad
Angle ∠ B = β = 43.24879853748° = 43°14'53″ = 0.75548197396 rad
Angle ∠ C = γ = 126.4565829383° = 126°27'21″ = 2.20770705811 rad

Height: ha = 18.4999249234
Height: hb = 4.82658911045
Height: hc = 4.11109442742

Median: ma = 24.9899799196
Median: mb = 15.81992920196
Median: mc = 10.01224921973

Inradius: r = 1.98220624179
Circumradius: R = 16.784446493

Vertex coordinates: A[27; 0] B[0; 0] C[4.37703703704; 4.11109442742]
Centroid: CG[10.45767901235; 1.37703147581]
Coordinates of the circumscribed circle: U[13.5; -9.9733377712]
Coordinates of the inscribed circle: I[5; 1.98220624179]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.7043814758° = 169°42'14″ = 0.18797023329 rad
∠ B' = β' = 136.7522014625° = 136°45'7″ = 0.75548197396 rad
∠ C' = γ' = 53.54441706172° = 53°32'39″ = 2.20770705811 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 6 ; ; b = 23 ; ; c = 27 ; ;

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

p = a+b+c = 6+23+27 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-6)(28-23)(28-27) } ; ; T = sqrt{ 3080 } = 55.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 55.5 }{ 6 } = 18.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 55.5 }{ 23 } = 4.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 55.5 }{ 27 } = 4.11 ; ;

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{ 6**2-23**2-27**2 }{ 2 * 23 * 27 } ) = 10° 17'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-6**2-27**2 }{ 2 * 6 * 27 } ) = 43° 14'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-6**2-23**2 }{ 2 * 23 * 6 } ) = 126° 27'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 55.5 }{ 28 } = 1.98 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 10° 17'46" } = 16.78 ; ;




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