23 26 29 triangle

Acute scalene triangle.

Sides: a = 23   b = 26   c = 29

Area: T = 284.8165729903
Perimeter: p = 78
Semiperimeter: s = 39

Angle ∠ A = α = 49.06772754258° = 49°4'2″ = 0.85663855112 rad
Angle ∠ B = β = 58.65216564476° = 58°39'6″ = 1.02436645168 rad
Angle ∠ C = γ = 72.28110681266° = 72°16'52″ = 1.26215426257 rad

Height: ha = 24.76765852089
Height: hb = 21.90989023002
Height: hc = 19.64224641312

Median: ma = 25.02549875125
Median: mb = 22.71656333832
Median: mc = 19.80553023203

Inradius: r = 7.30329674334
Circumradius: R = 15.2222122744

Vertex coordinates: A[29; 0] B[0; 0] C[11.96655172414; 19.64224641312]
Centroid: CG[13.65551724138; 6.54774880437]
Coordinates of the circumscribed circle: U[14.5; 4.63328199656]
Coordinates of the inscribed circle: I[13; 7.30329674334]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.9332724574° = 130°55'58″ = 0.85663855112 rad
∠ B' = β' = 121.3488343552° = 121°20'54″ = 1.02436645168 rad
∠ C' = γ' = 107.7198931873° = 107°43'8″ = 1.26215426257 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 = 23 ; ; b = 26 ; ; c = 29 ; ;

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

p = a+b+c = 23+26+29 = 78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 78 }{ 2 } = 39 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39 * (39-23)(39-26)(39-29) } ; ; T = sqrt{ 81120 } = 284.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 284.82 }{ 23 } = 24.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 284.82 }{ 26 } = 21.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 284.82 }{ 29 } = 19.64 ; ;

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{ 23**2-26**2-29**2 }{ 2 * 26 * 29 } ) = 49° 4'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-23**2-29**2 }{ 2 * 23 * 29 } ) = 58° 39'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-23**2-26**2 }{ 2 * 26 * 23 } ) = 72° 16'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 284.82 }{ 39 } = 7.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 23 }{ 2 * sin 49° 4'2" } = 15.22 ; ;




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