11 14 22 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 14   c = 22

Area: T = 64.6998821473
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 24.84223038214° = 24°50'32″ = 0.43435799955 rad
Angle ∠ B = β = 32.32436365082° = 32°19'25″ = 0.56441538833 rad
Angle ∠ C = γ = 122.834405967° = 122°50'3″ = 2.14438587748 rad

Height: ha = 11.7633422086
Height: hb = 9.24326887819
Height: hc = 5.8821711043

Median: ma = 17.65997159068
Median: mb = 15.92216833281
Median: mc = 6.1243724357

Inradius: r = 2.75331413393
Circumradius: R = 13.09114285719

Vertex coordinates: A[22; 0] B[0; 0] C[9.29554545455; 5.8821711043]
Centroid: CG[10.43218181818; 1.96105703477]
Coordinates of the circumscribed circle: U[11; -7.09882745828]
Coordinates of the inscribed circle: I[9.5; 2.75331413393]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.1587696179° = 155°9'28″ = 0.43435799955 rad
∠ B' = β' = 147.6766363492° = 147°40'35″ = 0.56441538833 rad
∠ C' = γ' = 57.16659403296° = 57°9'57″ = 2.14438587748 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 = 14 ; ; c = 22 ; ;

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

p = a+b+c = 11+14+22 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-11)(23.5-14)(23.5-22) } ; ; T = sqrt{ 4185.94 } = 64.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 64.7 }{ 11 } = 11.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 64.7 }{ 14 } = 9.24 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 64.7 }{ 22 } = 5.88 ; ;

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**2-14**2-22**2 }{ 2 * 14 * 22 } ) = 24° 50'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-11**2-22**2 }{ 2 * 11 * 22 } ) = 32° 19'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-11**2-14**2 }{ 2 * 14 * 11 } ) = 122° 50'3" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 64.7 }{ 23.5 } = 2.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 24° 50'32" } = 13.09 ; ;




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