19 23 30 triangle

Obtuse scalene triangle.

Sides: a = 19   b = 23   c = 30

Area: T = 218.4865697472
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 39.29334109792° = 39°17'36″ = 0.68657993959 rad
Angle ∠ B = β = 50.05110165987° = 50°3'4″ = 0.87435550336 rad
Angle ∠ C = γ = 90.65655724222° = 90°39'20″ = 1.5822238224 rad

Height: ha = 22.99884944708
Height: hb = 18.99987563019
Height: hc = 14.56657131648

Median: ma = 24.98549954973
Median: mb = 22.32215142855
Median: mc = 14.83223969742

Inradius: r = 6.0699047152
Circumradius: R = 15.00109819312

Vertex coordinates: A[30; 0] B[0; 0] C[12.2; 14.56657131648]
Centroid: CG[14.06766666667; 4.85552377216]
Coordinates of the circumscribed circle: U[15; -0.17216359489]
Coordinates of the inscribed circle: I[13; 6.0699047152]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.7076589021° = 140°42'24″ = 0.68657993959 rad
∠ B' = β' = 129.9498983401° = 129°56'56″ = 0.87435550336 rad
∠ C' = γ' = 89.34444275778° = 89°20'40″ = 1.5822238224 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 = 19 ; ; b = 23 ; ; c = 30 ; ;

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

p = a+b+c = 19+23+30 = 72 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-19)(36-23)(36-30) } ; ; T = sqrt{ 47736 } = 218.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 218.49 }{ 19 } = 23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 218.49 }{ 23 } = 19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 218.49 }{ 30 } = 14.57 ; ;

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{ 19**2-23**2-30**2 }{ 2 * 23 * 30 } ) = 39° 17'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-19**2-30**2 }{ 2 * 19 * 30 } ) = 50° 3'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-19**2-23**2 }{ 2 * 23 * 19 } ) = 90° 39'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 218.49 }{ 36 } = 6.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 39° 17'36" } = 15 ; ;




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