7 19 23 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 19   c = 23

Area: T = 59.47442591379
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 15.79548290504° = 15°47'41″ = 0.27656717717 rad
Angle ∠ B = β = 47.63302014306° = 47°37'49″ = 0.83113038384 rad
Angle ∠ C = γ = 116.5754969519° = 116°34'30″ = 2.03546170435 rad

Height: ha = 16.9932645468
Height: hb = 6.26604483303
Height: hc = 5.17216747076

Median: ma = 20.80326440627
Median: mb = 14.09878721799
Median: mc = 8.52993610546

Inradius: r = 2.42875207811
Circumradius: R = 12.85985040165

Vertex coordinates: A[23; 0] B[0; 0] C[4.71773913043; 5.17216747076]
Centroid: CG[9.23991304348; 1.72438915692]
Coordinates of the circumscribed circle: U[11.5; -5.75224886389]
Coordinates of the inscribed circle: I[5.5; 2.42875207811]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.205517095° = 164°12'19″ = 0.27656717717 rad
∠ B' = β' = 132.3769798569° = 132°22'11″ = 0.83113038384 rad
∠ C' = γ' = 63.4255030481° = 63°25'30″ = 2.03546170435 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 = 7 ; ; b = 19 ; ; c = 23 ; ;

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

p = a+b+c = 7+19+23 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-7)(24.5-19)(24.5-23) } ; ; T = sqrt{ 3537.19 } = 59.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.47 }{ 7 } = 16.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.47 }{ 19 } = 6.26 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.47 }{ 23 } = 5.17 ; ;

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{ 7**2-19**2-23**2 }{ 2 * 19 * 23 } ) = 15° 47'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-7**2-23**2 }{ 2 * 7 * 23 } ) = 47° 37'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-7**2-19**2 }{ 2 * 19 * 7 } ) = 116° 34'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.47 }{ 24.5 } = 2.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 15° 47'41" } = 12.86 ; ;




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