11 22 27 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 22   c = 27

Area: T = 116.9621532138
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 23.192176951° = 23°11'30″ = 0.40547727373 rad
Angle ∠ B = β = 51.96436260429° = 51°57'49″ = 0.90769363657 rad
Angle ∠ C = γ = 104.8454604447° = 104°50'41″ = 1.83298835506 rad

Height: ha = 21.26657331159
Height: hb = 10.6332866558
Height: hc = 8.66438171954

Median: ma = 24.00552077683
Median: mb = 17.43655957742
Median: mc = 10.96658560997

Inradius: r = 3.89987177379
Circumradius: R = 13.96661303178

Vertex coordinates: A[27; 0] B[0; 0] C[6.77877777778; 8.66438171954]
Centroid: CG[11.25992592593; 2.88879390651]
Coordinates of the circumscribed circle: U[13.5; -3.57880995029]
Coordinates of the inscribed circle: I[8; 3.89987177379]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.808823049° = 156°48'30″ = 0.40547727373 rad
∠ B' = β' = 128.0366373957° = 128°2'11″ = 0.90769363657 rad
∠ C' = γ' = 75.15553955529° = 75°9'19″ = 1.83298835506 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 = 27 ; ;

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

p = a+b+c = 11+22+27 = 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)(30-22)(30-27) } ; ; T = sqrt{ 13680 } = 116.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 116.96 }{ 11 } = 21.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 116.96 }{ 22 } = 10.63 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 116.96 }{ 27 } = 8.66 ; ;

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**2-27**2 }{ 2 * 22 * 27 } ) = 23° 11'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-11**2-27**2 }{ 2 * 11 * 27 } ) = 51° 57'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-11**2-22**2 }{ 2 * 22 * 11 } ) = 104° 50'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 116.96 }{ 30 } = 3.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 23° 11'30" } = 13.97 ; ;




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