19 26 29 triangle

Acute scalene triangle.

Sides: a = 19   b = 26   c = 29

Area: T = 242.0910892022
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 39.95223948559° = 39°57'9″ = 0.69773008343 rad
Angle ∠ B = β = 61.49898800871° = 61°29'24″ = 1.07332008642 rad
Angle ∠ C = γ = 78.5587725057° = 78°33'28″ = 1.37110909551 rad

Height: ha = 25.48332517918
Height: hb = 18.62223763094
Height: hc = 16.69659235877

Median: ma = 25.85105319094
Median: mb = 20.78546096908
Median: mc = 17.55770498661

Inradius: r = 6.54329970817
Circumradius: R = 14.79440303333

Vertex coordinates: A[29; 0] B[0; 0] C[9.06989655172; 16.69659235877]
Centroid: CG[12.69896551724; 5.56553078626]
Coordinates of the circumscribed circle: U[14.5; 2.93548481228]
Coordinates of the inscribed circle: I[11; 6.54329970817]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.0487605144° = 140°2'51″ = 0.69773008343 rad
∠ B' = β' = 118.5110119913° = 118°30'36″ = 1.07332008642 rad
∠ C' = γ' = 101.4422274943° = 101°26'32″ = 1.37110909551 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 = 19 ; ; b = 26 ; ; c = 29 ; ;

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

p = a+b+c = 19+26+29 = 74 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74 }{ 2 } = 37 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37 * (37-19)(37-26)(37-29) } ; ; T = sqrt{ 58608 } = 242.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 242.09 }{ 19 } = 25.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 242.09 }{ 26 } = 18.62 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 242.09 }{ 29 } = 16.7 ; ;

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{ 19**2-26**2-29**2 }{ 2 * 26 * 29 } ) = 39° 57'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-19**2-29**2 }{ 2 * 19 * 29 } ) = 61° 29'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-19**2-26**2 }{ 2 * 26 * 19 } ) = 78° 33'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 242.09 }{ 37 } = 6.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 39° 57'9" } = 14.79 ; ;




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