11 22 28 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 22   c = 28

Area: T = 112.4210805459
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 21.40877436432° = 21°24'28″ = 0.3743635612 rad
Angle ∠ B = β = 46.88768325263° = 46°53'13″ = 0.81883296034 rad
Angle ∠ C = γ = 111.705542383° = 111°42'20″ = 1.95496274382 rad

Height: ha = 20.44401464471
Height: hb = 10.22200732235
Height: hc = 8.03300575328

Median: ma = 24.57113247506
Median: mb = 18.2077141456
Median: mc = 10.32198837203

Inradius: r = 3.68659280478
Circumradius: R = 15.06883851898

Vertex coordinates: A[28; 0] B[0; 0] C[7.51878571429; 8.03300575328]
Centroid: CG[11.83992857143; 2.67766858443]
Coordinates of the circumscribed circle: U[14; -5.5732811878]
Coordinates of the inscribed circle: I[8.5; 3.68659280478]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.5922256357° = 158°35'32″ = 0.3743635612 rad
∠ B' = β' = 133.1133167474° = 133°6'47″ = 0.81883296034 rad
∠ C' = γ' = 68.29545761695° = 68°17'40″ = 1.95496274382 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 = 28 ; ;

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

p = a+b+c = 11+22+28 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-11)(30.5-22)(30.5-28) } ; ; T = sqrt{ 12638.44 } = 112.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 112.42 }{ 11 } = 20.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 112.42 }{ 22 } = 10.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 112.42 }{ 28 } = 8.03 ; ;

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**2-28**2 }{ 2 * 22 * 28 } ) = 21° 24'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-11**2-28**2 }{ 2 * 11 * 28 } ) = 46° 53'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-11**2-22**2 }{ 2 * 22 * 11 } ) = 111° 42'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 112.42 }{ 30.5 } = 3.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 21° 24'28" } = 15.07 ; ;




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