22 23 29 triangle

Acute scalene triangle.

Sides: a = 22   b = 23   c = 29

Area: T = 249.3199072676
Perimeter: p = 74
Semiperimeter: s = 37

Angle ∠ A = α = 48.38114781929° = 48°22'53″ = 0.84444160914 rad
Angle ∠ B = β = 51.40440427654° = 51°24'15″ = 0.89771697951 rad
Angle ∠ C = γ = 80.21444790417° = 80°12'52″ = 1.44000067671 rad

Height: ha = 22.66553702433
Height: hb = 21.68799193631
Height: hc = 17.19444188052

Median: ma = 23.74986841741
Median: mb = 23.02771578793
Median: mc = 17.21219144781

Inradius: r = 6.73883533156
Circumradius: R = 14.71440768679

Vertex coordinates: A[29; 0] B[0; 0] C[13.7244137931; 17.19444188052]
Centroid: CG[14.24113793103; 5.73114729351]
Coordinates of the circumscribed circle: U[14.5; 2.50108114835]
Coordinates of the inscribed circle: I[14; 6.73883533156]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.6198521807° = 131°37'7″ = 0.84444160914 rad
∠ B' = β' = 128.5965957235° = 128°35'45″ = 0.89771697951 rad
∠ C' = γ' = 99.78655209583° = 99°47'8″ = 1.44000067671 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 = 22 ; ; b = 23 ; ; c = 29 ; ;

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

p = a+b+c = 22+23+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 * (37-22)(37-23)(37-29) } ; ; T = sqrt{ 62160 } = 249.32 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 249.32 }{ 22 } = 22.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 249.32 }{ 23 } = 21.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 249.32 }{ 29 } = 17.19 ; ;

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{ 22**2-23**2-29**2 }{ 2 * 23 * 29 } ) = 48° 22'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 51° 24'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-22**2-23**2 }{ 2 * 23 * 22 } ) = 80° 12'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 249.32 }{ 37 } = 6.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 48° 22'53" } = 14.71 ; ;




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