14 20 29 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 20   c = 29

Area: T = 125.8910577487
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 25.7288385264° = 25°43'42″ = 0.44990450341 rad
Angle ∠ B = β = 38.32771349636° = 38°19'38″ = 0.6698934698 rad
Angle ∠ C = γ = 115.9444479772° = 115°56'40″ = 2.02436129215 rad

Height: ha = 17.98443682124
Height: hb = 12.58990577487
Height: hc = 8.68221087922

Median: ma = 23.90660661758
Median: mb = 20.45772725455
Median: mc = 9.36774969976

Inradius: r = 3.99765262694
Circumradius: R = 16.12551146871

Vertex coordinates: A[29; 0] B[0; 0] C[10.98327586207; 8.68221087922]
Centroid: CG[13.32875862069; 2.89440362641]
Coordinates of the circumscribed circle: U[14.5; -7.05547376756]
Coordinates of the inscribed circle: I[11.5; 3.99765262694]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.2721614736° = 154°16'18″ = 0.44990450341 rad
∠ B' = β' = 141.6732865036° = 141°40'22″ = 0.6698934698 rad
∠ C' = γ' = 64.05655202276° = 64°3'20″ = 2.02436129215 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 = 14 ; ; b = 20 ; ; c = 29 ; ;

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

p = a+b+c = 14+20+29 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-14)(31.5-20)(31.5-29) } ; ; T = sqrt{ 15848.44 } = 125.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 125.89 }{ 14 } = 17.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 125.89 }{ 20 } = 12.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 125.89 }{ 29 } = 8.68 ; ;

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{ 14**2-20**2-29**2 }{ 2 * 20 * 29 } ) = 25° 43'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-14**2-29**2 }{ 2 * 14 * 29 } ) = 38° 19'38" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-14**2-20**2 }{ 2 * 20 * 14 } ) = 115° 56'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 125.89 }{ 31.5 } = 4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 25° 43'42" } = 16.13 ; ;




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