9 14 19 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 14   c = 19

Area: T = 59.39769696197
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 26.52553520166° = 26°31'31″ = 0.46329547279 rad
Angle ∠ B = β = 44.00334273489° = 44°12″ = 0.76880046894 rad
Angle ∠ C = γ = 109.4711220634° = 109°28'16″ = 1.91106332362 rad

Height: ha = 13.19993265821
Height: hb = 8.48552813742
Height: hc = 6.25223125915

Median: ma = 16.077015868
Median: mb = 13.11548770486
Median: mc = 6.94662219947

Inradius: r = 2.82884271247
Circumradius: R = 10.07662716319

Vertex coordinates: A[19; 0] B[0; 0] C[6.47436842105; 6.25223125915]
Centroid: CG[8.49112280702; 2.08441041972]
Coordinates of the circumscribed circle: U[9.5; -3.35987572106]
Coordinates of the inscribed circle: I[7; 2.82884271247]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.4754647983° = 153°28'29″ = 0.46329547279 rad
∠ B' = β' = 135.9976572651° = 135°59'48″ = 0.76880046894 rad
∠ C' = γ' = 70.52987793655° = 70°31'44″ = 1.91106332362 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 = 9 ; ; b = 14 ; ; c = 19 ; ;

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

p = a+b+c = 9+14+19 = 42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42 }{ 2 } = 21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21 * (21-9)(21-14)(21-19) } ; ; T = sqrt{ 3528 } = 59.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.4 }{ 9 } = 13.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.4 }{ 14 } = 8.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.4 }{ 19 } = 6.25 ; ;

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**2-9**2 }{ 2 * 14 * 19 } ) = 26° 31'31" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 9**2+19**2-14**2 }{ 2 * 9 * 19 } ) = 44° 12" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 9**2+14**2-19**2 }{ 2 * 9 * 14 } ) = 109° 28'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.4 }{ 21 } = 2.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 26° 31'31" } = 10.08 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 19**2 - 9**2 } }{ 2 } = 16.07 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 19**2+2 * 9**2 - 14**2 } }{ 2 } = 13.115 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 9**2 - 19**2 } }{ 2 } = 6.946 ; ;
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