20 26 27 triangle

Acute scalene triangle.

Sides: a = 20   b = 26   c = 27

Area: T = 245.1010872092
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 44.29902177194° = 44°17'25″ = 0.77330101256 rad
Angle ∠ B = β = 65.22004820834° = 65°12'2″ = 1.13879630862 rad
Angle ∠ C = γ = 70.50993001972° = 70°30'33″ = 1.23106194417 rad

Height: ha = 24.51100872091
Height: hb = 18.85439132378
Height: hc = 18.15656201549

Median: ma = 24.54658754173
Median: mb = 19.88771818014
Median: mc = 18.86113361139

Inradius: r = 6.71550923861
Circumradius: R = 14.32106344802

Vertex coordinates: A[27; 0] B[0; 0] C[8.38988888889; 18.15656201549]
Centroid: CG[11.79662962963; 6.0521873385]
Coordinates of the circumscribed circle: U[13.5; 4.77881347737]
Coordinates of the inscribed circle: I[10.5; 6.71550923861]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.7109782281° = 135°42'35″ = 0.77330101256 rad
∠ B' = β' = 114.8799517917° = 114°47'58″ = 1.13879630862 rad
∠ C' = γ' = 109.4910699803° = 109°29'27″ = 1.23106194417 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 = 20 ; ; b = 26 ; ; c = 27 ; ;

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

p = a+b+c = 20+26+27 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-20)(36.5-26)(36.5-27) } ; ; T = sqrt{ 60074.44 } = 245.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 245.1 }{ 20 } = 24.51 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 245.1 }{ 26 } = 18.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 245.1 }{ 27 } = 18.16 ; ;

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{ 20**2-26**2-27**2 }{ 2 * 26 * 27 } ) = 44° 17'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-20**2-27**2 }{ 2 * 20 * 27 } ) = 65° 12'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-20**2-26**2 }{ 2 * 26 * 20 } ) = 70° 30'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 245.1 }{ 36.5 } = 6.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 20 }{ 2 * sin 44° 17'25" } = 14.32 ; ;




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