14 20 28 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 20   c = 28

Area: T = 131.8754940758
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 28.09880547134° = 28°5'53″ = 0.49904035682 rad
Angle ∠ B = β = 42.28659661512° = 42°17'9″ = 0.73880293367 rad
Angle ∠ C = γ = 109.6165979135° = 109°36'58″ = 1.91331597487 rad

Height: ha = 18.83992772512
Height: hb = 13.18774940758
Height: hc = 9.42196386256

Median: ma = 23.30223603955
Median: mb = 19.74884176581
Median: mc = 10.10995049384

Inradius: r = 4.2544030347
Circumradius: R = 14.86325659184

Vertex coordinates: A[28; 0] B[0; 0] C[10.35771428571; 9.42196386256]
Centroid: CG[12.78657142857; 3.14398795419]
Coordinates of the circumscribed circle: U[14; -4.99895757012]
Coordinates of the inscribed circle: I[11; 4.2544030347]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.9021945287° = 151°54'7″ = 0.49904035682 rad
∠ B' = β' = 137.7144033849° = 137°42'51″ = 0.73880293367 rad
∠ C' = γ' = 70.38440208646° = 70°23'2″ = 1.91331597487 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 = 28 ; ;

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

p = a+b+c = 14+20+28 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-14)(31-20)(31-28) } ; ; T = sqrt{ 17391 } = 131.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 131.87 }{ 14 } = 18.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 131.87 }{ 20 } = 13.19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 131.87 }{ 28 } = 9.42 ; ;

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**2-28**2 }{ 2 * 20 * 28 } ) = 28° 5'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-14**2-28**2 }{ 2 * 14 * 28 } ) = 42° 17'9" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-14**2-20**2 }{ 2 * 20 * 14 } ) = 109° 36'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 131.87 }{ 31 } = 4.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 28° 5'53" } = 14.86 ; ;




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