6 19 23 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 19   c = 23

Area: T = 46.47658001545
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 12.28108543959° = 12°16'51″ = 0.21443413442 rad
Angle ∠ B = β = 42.34326054522° = 42°20'33″ = 0.7399017879 rad
Angle ∠ C = γ = 125.3776540152° = 125°22'36″ = 2.18882334304 rad

Height: ha = 15.49219333848
Height: hb = 4.89221894899
Height: hc = 4.04113739265

Median: ma = 20.88106130178
Median: mb = 13.86554246239
Median: mc = 8.1399410298

Inradius: r = 1.93664916731
Circumradius: R = 14.10441143524

Vertex coordinates: A[23; 0] B[0; 0] C[4.43547826087; 4.04113739265]
Centroid: CG[9.14549275362; 1.34771246422]
Coordinates of the circumscribed circle: U[11.5; -8.16655398883]
Coordinates of the inscribed circle: I[5; 1.93664916731]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.7199145604° = 167°43'9″ = 0.21443413442 rad
∠ B' = β' = 137.6577394548° = 137°39'27″ = 0.7399017879 rad
∠ C' = γ' = 54.62334598481° = 54°37'24″ = 2.18882334304 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 = 23 ; ;

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

p = a+b+c = 6+19+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 * (24-6)(24-19)(24-23) } ; ; T = sqrt{ 2160 } = 46.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 46.48 }{ 6 } = 15.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 46.48 }{ 19 } = 4.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 46.48 }{ 23 } = 4.04 ; ;

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**2-23**2 }{ 2 * 19 * 23 } ) = 12° 16'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-6**2-23**2 }{ 2 * 6 * 23 } ) = 42° 20'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-6**2-19**2 }{ 2 * 19 * 6 } ) = 125° 22'36" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 46.48 }{ 24 } = 1.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 12° 16'51" } = 14.1 ; ;




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