11 22 29 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 22   c = 29

Area: T = 105.641090117
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 19.33993618163° = 19°20'22″ = 0.33875355389 rad
Angle ∠ B = β = 41.47774630076° = 41°28'39″ = 0.72439182949 rad
Angle ∠ C = γ = 119.1833175176° = 119°10'59″ = 2.08801388198 rad

Height: ha = 19.20774365764
Height: hb = 9.60437182882
Height: hc = 7.2865579391

Median: ma = 25.14545819214
Median: mb = 18.9743665961
Median: mc = 9.60546863561

Inradius: r = 3.40877710055
Circumradius: R = 16.60881506364

Vertex coordinates: A[29; 0] B[0; 0] C[8.24113793103; 7.2865579391]
Centroid: CG[12.41437931034; 2.42985264637]
Coordinates of the circumscribed circle: U[14.5; -8.09881891533]
Coordinates of the inscribed circle: I[9; 3.40877710055]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.6610638184° = 160°39'38″ = 0.33875355389 rad
∠ B' = β' = 138.5232536992° = 138°31'21″ = 0.72439182949 rad
∠ C' = γ' = 60.8176824824° = 60°49'1″ = 2.08801388198 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 = 22 ; ; c = 29 ; ;

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

p = a+b+c = 11+22+29 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-11)(31-22)(31-29) } ; ; T = sqrt{ 11160 } = 105.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 105.64 }{ 11 } = 19.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 105.64 }{ 22 } = 9.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 105.64 }{ 29 } = 7.29 ; ;

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**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 19° 20'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-11**2-29**2 }{ 2 * 11 * 29 } ) = 41° 28'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-11**2-22**2 }{ 2 * 22 * 11 } ) = 119° 10'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 105.64 }{ 31 } = 3.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 19° 20'22" } = 16.61 ; ;




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