10 11 19 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 11   c = 19

Area: T = 42.42664068712
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 23.95334516247° = 23°57'12″ = 0.41880665981 rad
Angle ∠ B = β = 26.52553520166° = 26°31'31″ = 0.46329547279 rad
Angle ∠ C = γ = 129.5211196359° = 129°31'16″ = 2.26105713276 rad

Height: ha = 8.48552813742
Height: hb = 7.71438921584
Height: hc = 4.46659375654

Median: ma = 14.69769384567
Median: mb = 14.15109716981
Median: mc = 4.5

Inradius: r = 2.12113203436
Circumradius: R = 12.31554431057

Vertex coordinates: A[19; 0] B[0; 0] C[8.94773684211; 4.46659375654]
Centroid: CG[9.31657894737; 1.48986458551]
Coordinates of the circumscribed circle: U[9.5; -7.83771001582]
Coordinates of the inscribed circle: I[9; 2.12113203436]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.0476548375° = 156°2'48″ = 0.41880665981 rad
∠ B' = β' = 153.4754647983° = 153°28'29″ = 0.46329547279 rad
∠ C' = γ' = 50.47988036414° = 50°28'44″ = 2.26105713276 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 = 10 ; ; b = 11 ; ; c = 19 ; ;

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

p = a+b+c = 10+11+19 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-10)(20-11)(20-19) } ; ; T = sqrt{ 1800 } = 42.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 42.43 }{ 10 } = 8.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 42.43 }{ 11 } = 7.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 42.43 }{ 19 } = 4.47 ; ;

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{ 10**2-11**2-19**2 }{ 2 * 11 * 19 } ) = 23° 57'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-10**2-19**2 }{ 2 * 10 * 19 } ) = 26° 31'31" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-10**2-11**2 }{ 2 * 11 * 10 } ) = 129° 31'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 42.43 }{ 20 } = 2.12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 23° 57'12" } = 12.32 ; ;




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