2 21 22 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 21   c = 22

Area: T = 18.59993951515
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 4.6188275596° = 4°37'6″ = 0.08106041149 rad
Angle ∠ B = β = 57.71877199078° = 57°43'4″ = 1.00773642491 rad
Angle ∠ C = γ = 117.6644004496° = 117°39'50″ = 2.05436242895 rad

Height: ha = 18.59993951515
Height: hb = 1.77113709668
Height: hc = 1.69108541047

Median: ma = 21.48325510589
Median: mb = 11.56550335062
Median: mc = 10.07547208398

Inradius: r = 0.82766397845
Circumradius: R = 12.42197587136

Vertex coordinates: A[22; 0] B[0; 0] C[1.06881818182; 1.69108541047]
Centroid: CG[7.68993939394; 0.56436180349]
Coordinates of the circumscribed circle: U[11; -5.76663165456]
Coordinates of the inscribed circle: I[1.5; 0.82766397845]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.3821724404° = 175°22'54″ = 0.08106041149 rad
∠ B' = β' = 122.2822280092° = 122°16'56″ = 1.00773642491 rad
∠ C' = γ' = 62.33659955038° = 62°20'10″ = 2.05436242895 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 = 2 ; ; b = 21 ; ; c = 22 ; ;

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

p = a+b+c = 2+21+22 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-2)(22.5-21)(22.5-22) } ; ; T = sqrt{ 345.94 } = 18.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18.6 }{ 2 } = 18.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18.6 }{ 21 } = 1.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18.6 }{ 22 } = 1.69 ; ;

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{ 2**2-21**2-22**2 }{ 2 * 21 * 22 } ) = 4° 37'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-2**2-22**2 }{ 2 * 2 * 22 } ) = 57° 43'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-2**2-21**2 }{ 2 * 21 * 2 } ) = 117° 39'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18.6 }{ 22.5 } = 0.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 4° 37'6" } = 12.42 ; ;




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