14 19 22 triangle

Acute scalene triangle.

Sides: a = 14   b = 19   c = 22

Area: T = 131.7421935237
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 39.07655206502° = 39°4'32″ = 0.68219964923 rad
Angle ∠ B = β = 58.81113776665° = 58°48'41″ = 1.02664521779 rad
Angle ∠ C = γ = 82.11331016833° = 82°6'47″ = 1.43331439834 rad

Height: ha = 18.82202764624
Height: hb = 13.86875721302
Height: hc = 11.9776539567

Median: ma = 19.32661480901
Median: mb = 15.80334806293
Median: mc = 12.5549900398

Inradius: r = 4.79106158268
Circumradius: R = 11.10550440952

Vertex coordinates: A[22; 0] B[0; 0] C[7.25; 11.9776539567]
Centroid: CG[9.75; 3.99221798557]
Coordinates of the circumscribed circle: U[11; 1.52438124416]
Coordinates of the inscribed circle: I[8.5; 4.79106158268]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.924447935° = 140°55'28″ = 0.68219964923 rad
∠ B' = β' = 121.1898622333° = 121°11'19″ = 1.02664521779 rad
∠ C' = γ' = 97.88768983167° = 97°53'13″ = 1.43331439834 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 = 14 ; ; b = 19 ; ; c = 22 ; ;

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

p = a+b+c = 14+19+22 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-14)(27.5-19)(27.5-22) } ; ; T = sqrt{ 17355.94 } = 131.74 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 131.74 }{ 14 } = 18.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 131.74 }{ 19 } = 13.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 131.74 }{ 22 } = 11.98 ; ;

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{ 14**2-19**2-22**2 }{ 2 * 19 * 22 } ) = 39° 4'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-14**2-22**2 }{ 2 * 14 * 22 } ) = 58° 48'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-14**2-19**2 }{ 2 * 19 * 14 } ) = 82° 6'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 131.74 }{ 27.5 } = 4.79 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 39° 4'32" } = 11.11 ; ;




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