8 14 20 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 14   c = 20

Area: T = 43.71549859888
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 18.19548723388° = 18°11'42″ = 0.31875604293 rad
Angle ∠ B = β = 33.12329402077° = 33°7'23″ = 0.57881043646 rad
Angle ∠ C = γ = 128.6822187453° = 128°40'56″ = 2.24659278597 rad

Height: ha = 10.92987464972
Height: hb = 6.24549979984
Height: hc = 4.37114985989

Median: ma = 16.79328556237
Median: mb = 13.52877492585
Median: mc = 5.47772255751

Inradius: r = 2.08216659995
Circumradius: R = 12.81102523044

Vertex coordinates: A[20; 0] B[0; 0] C[6.7; 4.37114985989]
Centroid: CG[8.9; 1.45771661996]
Coordinates of the circumscribed circle: U[10; -8.00664076903]
Coordinates of the inscribed circle: I[7; 2.08216659995]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.8055127661° = 161°48'18″ = 0.31875604293 rad
∠ B' = β' = 146.8777059792° = 146°52'37″ = 0.57881043646 rad
∠ C' = γ' = 51.31878125465° = 51°19'4″ = 2.24659278597 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 = 8 ; ; b = 14 ; ; c = 20 ; ;

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

p = a+b+c = 8+14+20 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-8)(21-14)(21-20) } ; ; T = sqrt{ 1911 } = 43.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 43.71 }{ 8 } = 10.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 43.71 }{ 14 } = 6.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 43.71 }{ 20 } = 4.37 ; ;

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{ 8**2-14**2-20**2 }{ 2 * 14 * 20 } ) = 18° 11'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-8**2-20**2 }{ 2 * 8 * 20 } ) = 33° 7'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-8**2-14**2 }{ 2 * 14 * 8 } ) = 128° 40'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 43.71 }{ 21 } = 2.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 18° 11'42" } = 12.81 ; ;




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