8 14 19 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 14   c = 19

Area: T = 49.98443725578
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 22.07551482086° = 22°4'31″ = 0.38552840191 rad
Angle ∠ B = β = 41.1243868612° = 41°7'26″ = 0.71877469084 rad
Angle ∠ C = γ = 116.8010983179° = 116°48'4″ = 2.0398561726 rad

Height: ha = 12.49660931395
Height: hb = 7.14106246511
Height: hc = 5.26215129008

Median: ma = 16.2021851746
Median: mb = 12.78767118525
Median: mc = 6.30547601065

Inradius: r = 2.4388262076
Circumradius: R = 10.64333265594

Vertex coordinates: A[19; 0] B[0; 0] C[6.02663157895; 5.26215129008]
Centroid: CG[8.34221052632; 1.75438376336]
Coordinates of the circumscribed circle: U[9.5; -4.79989999219]
Coordinates of the inscribed circle: I[6.5; 2.4388262076]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.9254851791° = 157°55'29″ = 0.38552840191 rad
∠ B' = β' = 138.8766131388° = 138°52'34″ = 0.71877469084 rad
∠ C' = γ' = 63.19990168207° = 63°11'56″ = 2.0398561726 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 = 8 ; ; b = 14 ; ; c = 19 ; ;

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

p = a+b+c = 8+14+19 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-8)(20.5-14)(20.5-19) } ; ; T = sqrt{ 2498.44 } = 49.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 49.98 }{ 8 } = 12.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 49.98 }{ 14 } = 7.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 49.98 }{ 19 } = 5.26 ; ;

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{ 8**2-14**2-19**2 }{ 2 * 14 * 19 } ) = 22° 4'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-8**2-19**2 }{ 2 * 8 * 19 } ) = 41° 7'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-8**2-14**2 }{ 2 * 14 * 8 } ) = 116° 48'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 49.98 }{ 20.5 } = 2.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 22° 4'31" } = 10.64 ; ;




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