11 20 28 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 20   c = 28

Area: T = 88.18769463129
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 18.35879993921° = 18°21'29″ = 0.32204075335 rad
Angle ∠ B = β = 34.93547022415° = 34°56'5″ = 0.61097255773 rad
Angle ∠ C = γ = 126.7077298366° = 126°42'26″ = 2.21114595428 rad

Height: ha = 16.03439902387
Height: hb = 8.81986946313
Height: hc = 6.29990675938

Median: ma = 23.7011265789
Median: mb = 18.77549833555
Median: mc = 8.03111892021

Inradius: r = 2.98993880106
Circumradius: R = 17.46329019871

Vertex coordinates: A[28; 0] B[0; 0] C[9.01878571429; 6.29990675938]
Centroid: CG[12.33992857143; 2.10996891979]
Coordinates of the circumscribed circle: U[14; -10.43880527786]
Coordinates of the inscribed circle: I[9.5; 2.98993880106]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.6422000608° = 161°38'31″ = 0.32204075335 rad
∠ B' = β' = 145.0655297758° = 145°3'55″ = 0.61097255773 rad
∠ C' = γ' = 53.29327016337° = 53°17'34″ = 2.21114595428 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 = 28 ; ;

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

p = a+b+c = 11+20+28 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-11)(29.5-20)(29.5-28) } ; ; T = sqrt{ 7776.94 } = 88.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 88.19 }{ 11 } = 16.03 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 88.19 }{ 20 } = 8.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 88.19 }{ 28 } = 6.3 ; ;

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**2-28**2 }{ 2 * 20 * 28 } ) = 18° 21'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-11**2-28**2 }{ 2 * 11 * 28 } ) = 34° 56'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-11**2-20**2 }{ 2 * 20 * 11 } ) = 126° 42'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 88.19 }{ 29.5 } = 2.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 18° 21'29" } = 17.46 ; ;




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