5 15 19 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 15   c = 19

Area: T = 25.22327575812
Perimeter: p = 39
Semiperimeter: s = 19.5

Angle ∠ A = α = 10.19551720375° = 10°11'43″ = 0.17879393199 rad
Angle ∠ B = β = 32.07334123921° = 32°4'24″ = 0.56597866486 rad
Angle ∠ C = γ = 137.731141557° = 137°43'53″ = 2.40438666851 rad

Height: ha = 10.08991030325
Height: hb = 3.36330343442
Height: hc = 2.65550271138

Median: ma = 16.93436942219
Median: mb = 11.69440155635
Median: mc = 5.89549130613

Inradius: r = 1.29334747478
Circumradius: R = 14.12441495444

Vertex coordinates: A[19; 0] B[0; 0] C[4.23768421053; 2.65550271138]
Centroid: CG[7.74656140351; 0.88550090379]
Coordinates of the circumscribed circle: U[9.5; -10.45218706629]
Coordinates of the inscribed circle: I[4.5; 1.29334747478]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.8054827963° = 169°48'17″ = 0.17879393199 rad
∠ B' = β' = 147.9276587608° = 147°55'36″ = 0.56597866486 rad
∠ C' = γ' = 42.26985844296° = 42°16'7″ = 2.40438666851 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 = 5 ; ; b = 15 ; ; c = 19 ; ;

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

p = a+b+c = 5+15+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 * (19.5-5)(19.5-15)(19.5-19) } ; ; T = sqrt{ 636.19 } = 25.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25.22 }{ 5 } = 10.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25.22 }{ 15 } = 3.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25.22 }{ 19 } = 2.66 ; ;

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{ 5**2-15**2-19**2 }{ 2 * 15 * 19 } ) = 10° 11'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-5**2-19**2 }{ 2 * 5 * 19 } ) = 32° 4'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-5**2-15**2 }{ 2 * 15 * 5 } ) = 137° 43'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25.22 }{ 19.5 } = 1.29 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 10° 11'43" } = 14.12 ; ;




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