2 18 19 triangle

Obtuse scalene triangle.

Sides: a = 2   b = 18   c = 19

Area: T = 15.99880467558
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 5.36882046992° = 5°22'6″ = 0.09436928469 rad
Angle ∠ B = β = 57.35221825649° = 57°21'8″ = 1.0010984419 rad
Angle ∠ C = γ = 117.2879612736° = 117°16'47″ = 2.04769153877 rad

Height: ha = 15.99880467558
Height: hb = 1.77875607506
Height: hc = 1.68440049217

Median: ma = 18.48797186126
Median: mb = 10.07547208398
Median: mc = 8.58877820187

Inradius: r = 0.82204126541
Circumradius: R = 10.68988048654

Vertex coordinates: A[19; 0] B[0; 0] C[1.07989473684; 1.68440049217]
Centroid: CG[6.69329824561; 0.56113349739]
Coordinates of the circumscribed circle: U[9.5; -4.89990355633]
Coordinates of the inscribed circle: I[1.5; 0.82204126541]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.6321795301° = 174°37'54″ = 0.09436928469 rad
∠ B' = β' = 122.6487817435° = 122°38'52″ = 1.0010984419 rad
∠ C' = γ' = 62.7220387264° = 62°43'13″ = 2.04769153877 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 = 2 ; ; b = 18 ; ; c = 19 ; ;

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

p = a+b+c = 2+18+19 = 39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 39 }{ 2 } = 19.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19.5 * (19.5-2)(19.5-18)(19.5-19) } ; ; T = sqrt{ 255.94 } = 16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16 }{ 2 } = 16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16 }{ 18 } = 1.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16 }{ 19 } = 1.68 ; ;

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{ 2**2-18**2-19**2 }{ 2 * 18 * 19 } ) = 5° 22'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-2**2-19**2 }{ 2 * 2 * 19 } ) = 57° 21'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-2**2-18**2 }{ 2 * 18 * 2 } ) = 117° 16'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16 }{ 19.5 } = 0.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 5° 22'6" } = 10.69 ; ;




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