6 16 19 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 16   c = 19

Area: T = 44.79332751649
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 17.13991052292° = 17°8'21″ = 0.29991338171 rad
Angle ∠ B = β = 51.79990771692° = 51°47'57″ = 0.90440644461 rad
Angle ∠ C = γ = 111.0621817602° = 111°3'43″ = 1.93883943904 rad

Height: ha = 14.93110917216
Height: hb = 5.59991593956
Height: hc = 4.71550815963

Median: ma = 17.30660682999
Median: mb = 11.59774135047
Median: mc = 7.46765922615

Inradius: r = 2.18550378129
Circumradius: R = 10.18800995422

Vertex coordinates: A[19; 0] B[0; 0] C[3.71105263158; 4.71550815963]
Centroid: CG[7.57701754386; 1.57216938654]
Coordinates of the circumscribed circle: U[9.5; -3.6588473273]
Coordinates of the inscribed circle: I[4.5; 2.18550378129]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.8610894771° = 162°51'39″ = 0.29991338171 rad
∠ B' = β' = 128.2010922831° = 128°12'3″ = 0.90440644461 rad
∠ C' = γ' = 68.93881823984° = 68°56'17″ = 1.93883943904 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 = 16 ; ; c = 19 ; ;

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

p = a+b+c = 6+16+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 * (20.5-6)(20.5-16)(20.5-19) } ; ; T = sqrt{ 2006.44 } = 44.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.79 }{ 6 } = 14.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.79 }{ 16 } = 5.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.79 }{ 19 } = 4.72 ; ;

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{ 6**2-16**2-19**2 }{ 2 * 16 * 19 } ) = 17° 8'21" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-6**2-19**2 }{ 2 * 6 * 19 } ) = 51° 47'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-6**2-16**2 }{ 2 * 16 * 6 } ) = 111° 3'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.79 }{ 20.5 } = 2.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 17° 8'21" } = 10.18 ; ;




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