6 14 19 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 14   c = 19

Area: T = 26.9066086672
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 11.67215712088° = 11°40'18″ = 0.20437073465 rad
Angle ∠ B = β = 28.16765785968° = 28°10' = 0.49215995355 rad
Angle ∠ C = γ = 140.1621850194° = 140°9'43″ = 2.44662857716 rad

Height: ha = 8.96986955573
Height: hb = 3.84437266674
Height: hc = 2.83222196497

Median: ma = 16.41664551594
Median: mb = 12.22770192606
Median: mc = 5.07444457825

Inradius: r = 1.38797993165
Circumradius: R = 14.82993583108

Vertex coordinates: A[19; 0] B[0; 0] C[5.28994736842; 2.83222196497]
Centroid: CG[8.09664912281; 0.94440732166]
Coordinates of the circumscribed circle: U[9.5; -11.38768287029]
Coordinates of the inscribed circle: I[5.5; 1.38797993165]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.3288428791° = 168°19'42″ = 0.20437073465 rad
∠ B' = β' = 151.8333421403° = 151°50' = 0.49215995355 rad
∠ C' = γ' = 39.83881498056° = 39°50'17″ = 2.44662857716 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 = 6 ; ; b = 14 ; ; c = 19 ; ;

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

p = a+b+c = 6+14+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 * (19.5-6)(19.5-14)(19.5-19) } ; ; T = sqrt{ 723.94 } = 26.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26.91 }{ 6 } = 8.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26.91 }{ 14 } = 3.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26.91 }{ 19 } = 2.83 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 14**2+19**2-6**2 }{ 2 * 14 * 19 } ) = 11° 40'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+19**2-14**2 }{ 2 * 6 * 19 } ) = 28° 10' ; ; gamma = 180° - alpha - beta = 180° - 11° 40'18" - 28° 10' = 140° 9'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26.91 }{ 19.5 } = 1.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 11° 40'18" } = 14.83 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 19**2 - 6**2 } }{ 2 } = 16.416 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 19**2+2 * 6**2 - 14**2 } }{ 2 } = 12.227 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 6**2 - 19**2 } }{ 2 } = 5.074 ; ;
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