6 19 22 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 19   c = 22

Area: T = 52.68771663691
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 14.60113231096° = 14°36'5″ = 0.25548411634 rad
Angle ∠ B = β = 52.9677156255° = 52°58'2″ = 0.92444512721 rad
Angle ∠ C = γ = 112.4321520635° = 112°25'53″ = 1.96223002181 rad

Height: ha = 17.56223887897
Height: hb = 5.54660175125
Height: hc = 4.79897423972

Median: ma = 20.33546994077
Median: mb = 13.02988142208
Median: mc = 8.80334084308

Inradius: r = 2.24220070795
Circumradius: R = 11.99004312285

Vertex coordinates: A[22; 0] B[0; 0] C[3.61436363636; 4.79897423972]
Centroid: CG[8.53878787879; 1.59765807991]
Coordinates of the circumscribed circle: U[11; -4.54109540214]
Coordinates of the inscribed circle: I[4.5; 2.24220070795]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.399867689° = 165°23'55″ = 0.25548411634 rad
∠ B' = β' = 127.0332843745° = 127°1'58″ = 0.92444512721 rad
∠ C' = γ' = 67.56884793646° = 67°34'7″ = 1.96223002181 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 = 6 ; ; b = 19 ; ; c = 22 ; ;

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

p = a+b+c = 6+19+22 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-6)(23.5-19)(23.5-22) } ; ; T = sqrt{ 2775.94 } = 52.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 52.69 }{ 6 } = 17.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 52.69 }{ 19 } = 5.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 52.69 }{ 22 } = 4.79 ; ;

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{ 6**2-19**2-22**2 }{ 2 * 19 * 22 } ) = 14° 36'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-6**2-22**2 }{ 2 * 6 * 22 } ) = 52° 58'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-6**2-19**2 }{ 2 * 19 * 6 } ) = 112° 25'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 52.69 }{ 23.5 } = 2.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 14° 36'5" } = 11.9 ; ;




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