8 23 27 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 23   c = 27

Area: T = 85.48768410927
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 15.98110813462° = 15°58'52″ = 0.27989224875 rad
Angle ∠ B = β = 52.33301130357° = 52°19'48″ = 0.91333327704 rad
Angle ∠ C = γ = 111.6898805618° = 111°41'20″ = 1.94993373957 rad

Height: ha = 21.37217102732
Height: hb = 7.43436383559
Height: hc = 6.33223585995

Median: ma = 24.75988368063
Median: mb = 16.2565768207
Median: mc = 10.68987791632

Inradius: r = 2.94878221066
Circumradius: R = 14.52985518113

Vertex coordinates: A[27; 0] B[0; 0] C[4.88988888889; 6.33223585995]
Centroid: CG[10.63296296296; 2.11107861998]
Coordinates of the circumscribed circle: U[13.5; -5.36992474085]
Coordinates of the inscribed circle: I[6; 2.94878221066]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.0198918654° = 164°1'8″ = 0.27989224875 rad
∠ B' = β' = 127.6769886964° = 127°40'12″ = 0.91333327704 rad
∠ C' = γ' = 68.31111943819° = 68°18'40″ = 1.94993373957 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 = 8 ; ; b = 23 ; ; c = 27 ; ;

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

p = a+b+c = 8+23+27 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-8)(29-23)(29-27) } ; ; T = sqrt{ 7308 } = 85.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 85.49 }{ 8 } = 21.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 85.49 }{ 23 } = 7.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 85.49 }{ 27 } = 6.33 ; ;

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{ 8**2-23**2-27**2 }{ 2 * 23 * 27 } ) = 15° 58'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-8**2-27**2 }{ 2 * 8 * 27 } ) = 52° 19'48" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-8**2-23**2 }{ 2 * 23 * 8 } ) = 111° 41'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 85.49 }{ 29 } = 2.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 15° 58'52" } = 14.53 ; ;




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