11 19 22 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 19   c = 22

Area: T = 104.4998803821
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 309.9996213473° = 29°59'59″ = 0.52435921669 rad
Angle ∠ B = β = 59.7266235121° = 59°43'34″ = 1.04224194527 rad
Angle ∠ C = γ = 90.27441435317° = 90°16'27″ = 1.5765581034 rad

Height: ha = 198.9997825129
Height: hb = 110.9998740864
Height: hc = 9.54998912564

Median: ma = 19.80553023203
Median: mb = 14.56988022843
Median: mc = 10.95444511501

Inradius: r = 4.01991847623
Circumradius: R = 111.000125915

Vertex coordinates: A[22; 0] B[0; 0] C[5.54554545455; 9.54998912564]
Centroid: CG[9.18218181818; 3.16766304188]
Coordinates of the circumscribed circle: U[11; -0.05326321814]
Coordinates of the inscribed circle: I[7; 4.01991847623]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1500.000378653° = 150°1″ = 0.52435921669 rad
∠ B' = β' = 120.2743764879° = 120°16'26″ = 1.04224194527 rad
∠ C' = γ' = 89.72658564683° = 89°43'33″ = 1.5765581034 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 = 11 ; ; b = 19 ; ; c = 22 ; ;

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

p = a+b+c = 11+19+22 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-11)(26-19)(26-22) } ; ; T = sqrt{ 10920 } = 104.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 104.5 }{ 11 } = 19 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 104.5 }{ 19 } = 11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 104.5 }{ 22 } = 9.5 ; ;

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{ 11**2-19**2-22**2 }{ 2 * 19 * 22 } ) = 29° 59'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-11**2-22**2 }{ 2 * 11 * 22 } ) = 59° 43'34" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-11**2-19**2 }{ 2 * 19 * 11 } ) = 90° 16'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 104.5 }{ 26 } = 4.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 29° 59'59" } = 11 ; ;




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