11 20 29 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 20   c = 29

Area: T = 75.49883443527
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 15.09901851794° = 15°5'25″ = 0.26333734161 rad
Angle ∠ B = β = 28.25215730478° = 28°15'6″ = 0.49330829686 rad
Angle ∠ C = γ = 136.6588241773° = 136°39'30″ = 2.38551362689 rad

Height: ha = 13.72769717005
Height: hb = 7.55498344353
Height: hc = 5.20767823692

Median: ma = 24.29550612265
Median: mb = 19.51992212959
Median: mc = 7.08987234394

Inradius: r = 2.51766114784
Circumradius: R = 21.12662910952

Vertex coordinates: A[29; 0] B[0; 0] C[9.69896551724; 5.20767823692]
Centroid: CG[12.89765517241; 1.73655941231]
Coordinates of the circumscribed circle: U[14.5; -15.3654575342]
Coordinates of the inscribed circle: I[10; 2.51766114784]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.9109814821° = 164°54'35″ = 0.26333734161 rad
∠ B' = β' = 151.7488426952° = 151°44'54″ = 0.49330829686 rad
∠ C' = γ' = 43.34217582272° = 43°20'30″ = 2.38551362689 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 = 20 ; ; c = 29 ; ;

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

p = a+b+c = 11+20+29 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-11)(30-20)(30-29) } ; ; T = sqrt{ 5700 } = 75.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 75.5 }{ 11 } = 13.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 75.5 }{ 20 } = 7.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 75.5 }{ 29 } = 5.21 ; ;

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**2-20**2-29**2 }{ 2 * 20 * 29 } ) = 15° 5'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-11**2-29**2 }{ 2 * 11 * 29 } ) = 28° 15'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-11**2-20**2 }{ 2 * 20 * 11 } ) = 136° 39'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 75.5 }{ 30 } = 2.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 15° 5'25" } = 21.13 ; ;




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