11 19 23 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 19   c = 23

Area: T = 103.8377312658
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 28.37441945297° = 28°22'27″ = 0.49552231171 rad
Angle ∠ B = β = 55.17698043554° = 55°10'11″ = 0.96328947337 rad
Angle ∠ C = γ = 96.45660011149° = 96°27'22″ = 1.68334748028 rad

Height: ha = 18.88795113923
Height: hb = 10.93302434377
Height: hc = 9.02993315355

Median: ma = 20.36554118544
Median: mb = 15.3221553446
Median: mc = 10.42883268073

Inradius: r = 3.91883891569
Circumradius: R = 11.57333927356

Vertex coordinates: A[23; 0] B[0; 0] C[6.28326086957; 9.02993315355]
Centroid: CG[9.76108695652; 3.01097771785]
Coordinates of the circumscribed circle: U[11.5; -1.30113144942]
Coordinates of the inscribed circle: I[7.5; 3.91883891569]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.626580547° = 151°37'33″ = 0.49552231171 rad
∠ B' = β' = 124.8330195645° = 124°49'49″ = 0.96328947337 rad
∠ C' = γ' = 83.54439988851° = 83°32'38″ = 1.68334748028 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 = 11 ; ; b = 19 ; ; c = 23 ; ;

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

p = a+b+c = 11+19+23 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-11)(26.5-19)(26.5-23) } ; ; T = sqrt{ 10782.19 } = 103.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 103.84 }{ 11 } = 18.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 103.84 }{ 19 } = 10.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 103.84 }{ 23 } = 9.03 ; ;

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{ 11**2-19**2-23**2 }{ 2 * 19 * 23 } ) = 28° 22'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-11**2-23**2 }{ 2 * 11 * 23 } ) = 55° 10'11" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-11**2-19**2 }{ 2 * 19 * 11 } ) = 96° 27'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 103.84 }{ 26.5 } = 3.92 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 28° 22'27" } = 11.57 ; ;




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