20 22 26 triangle

Acute scalene triangle.

Sides: a = 20   b = 22   c = 26

Area: T = 213.7666227454
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 48.36986204606° = 48°22'7″ = 0.84441916817 rad
Angle ∠ B = β = 55.30333976437° = 55°18'12″ = 0.96552263764 rad
Angle ∠ C = γ = 76.32879818956° = 76°19'41″ = 1.33221745955 rad

Height: ha = 21.37766227454
Height: hb = 19.43332934049
Height: hc = 16.4443555958

Median: ma = 21.90989023002
Median: mb = 20.42105778567
Median: mc = 16.52327116419

Inradius: r = 6.28772419839
Circumradius: R = 13.37991012456

Vertex coordinates: A[26; 0] B[0; 0] C[11.38546153846; 16.4443555958]
Centroid: CG[12.46215384615; 5.48111853193]
Coordinates of the circumscribed circle: U[13; 3.16223330217]
Coordinates of the inscribed circle: I[12; 6.28772419839]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.6311379539° = 131°37'53″ = 0.84441916817 rad
∠ B' = β' = 124.6976602356° = 124°41'48″ = 0.96552263764 rad
∠ C' = γ' = 103.6722018104° = 103°40'19″ = 1.33221745955 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 = 22 ; ; c = 26 ; ;

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

p = a+b+c = 20+22+26 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-20)(34-22)(34-26) } ; ; T = sqrt{ 45696 } = 213.77 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 213.77 }{ 20 } = 21.38 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 213.77 }{ 22 } = 19.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 213.77 }{ 26 } = 16.44 ; ;

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**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 48° 22'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-20**2-26**2 }{ 2 * 20 * 26 } ) = 55° 18'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-20**2-22**2 }{ 2 * 22 * 20 } ) = 76° 19'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 213.77 }{ 34 } = 6.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 20 }{ 2 * sin 48° 22'7" } = 13.38 ; ;




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