3 22 23 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 22   c = 23

Area: T = 31.74990157328
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 7.20990639741° = 7°12'33″ = 0.12658219023 rad
Angle ∠ B = β = 66.96443158941° = 66°57'52″ = 1.16987477937 rad
Angle ∠ C = γ = 105.8276620132° = 105°49'36″ = 1.84770229576 rad

Height: ha = 21.16660104885
Height: hb = 2.88662741575
Height: hc = 2.76107839768

Median: ma = 22.45655115729
Median: mb = 12.16655250606
Median: mc = 10.68987791632

Inradius: r = 1.32328756555
Circumradius: R = 11.95331264589

Vertex coordinates: A[23; 0] B[0; 0] C[1.17439130435; 2.76107839768]
Centroid: CG[8.05879710145; 0.92202613256]
Coordinates of the circumscribed circle: U[11.5; -3.26599435797]
Coordinates of the inscribed circle: I[2; 1.32328756555]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 172.7910936026° = 172°47'27″ = 0.12658219023 rad
∠ B' = β' = 113.0365684106° = 113°2'8″ = 1.16987477937 rad
∠ C' = γ' = 74.17333798681° = 74°10'24″ = 1.84770229576 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 = 3 ; ; b = 22 ; ; c = 23 ; ;

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

p = a+b+c = 3+22+23 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-3)(24-22)(24-23) } ; ; T = sqrt{ 1008 } = 31.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 31.75 }{ 3 } = 21.17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 31.75 }{ 22 } = 2.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 31.75 }{ 23 } = 2.76 ; ;

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{ 3**2-22**2-23**2 }{ 2 * 22 * 23 } ) = 7° 12'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-3**2-23**2 }{ 2 * 3 * 23 } ) = 66° 57'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-3**2-22**2 }{ 2 * 22 * 3 } ) = 105° 49'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 31.75 }{ 24 } = 1.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 7° 12'33" } = 11.95 ; ;




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