8 23 29 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 23   c = 29

Area: T = 67.97105818719
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 11.76598371264° = 11°45'35″ = 0.20552478774 rad
Angle ∠ B = β = 35.87703643042° = 35°52'13″ = 0.6266055961 rad
Angle ∠ C = γ = 132.3769798569° = 132°22'11″ = 2.31102888152 rad

Height: ha = 16.9932645468
Height: hb = 5.91104853802
Height: hc = 4.6887626336

Median: ma = 25.86550343128
Median: mb = 17.89655301682
Median: mc = 9.28770878105

Inradius: r = 2.26656860624
Circumradius: R = 19.62661377093

Vertex coordinates: A[29; 0] B[0; 0] C[6.48327586207; 4.6887626336]
Centroid: CG[11.82875862069; 1.5632542112]
Coordinates of the circumscribed circle: U[14.5; -13.22663101954]
Coordinates of the inscribed circle: I[7; 2.26656860624]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.2440162874° = 168°14'25″ = 0.20552478774 rad
∠ B' = β' = 144.1329635696° = 144°7'47″ = 0.6266055961 rad
∠ C' = γ' = 47.63302014306° = 47°37'49″ = 2.31102888152 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 = 29 ; ;

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

p = a+b+c = 8+23+29 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-8)(30-23)(30-29) } ; ; T = sqrt{ 4620 } = 67.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 67.97 }{ 8 } = 16.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 67.97 }{ 23 } = 5.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 67.97 }{ 29 } = 4.69 ; ;

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**2-29**2 }{ 2 * 23 * 29 } ) = 11° 45'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-8**2-29**2 }{ 2 * 8 * 29 } ) = 35° 52'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-8**2-23**2 }{ 2 * 23 * 8 } ) = 132° 22'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 67.97 }{ 30 } = 2.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 11° 45'35" } = 19.63 ; ;




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