6 9 11 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 9   c = 11

Area: T = 26.98114751265
Perimeter: p = 26
Semiperimeter: s = 13

Angle ∠ A = α = 33.03301516046° = 33°1'49″ = 0.57664848979 rad
Angle ∠ B = β = 54.84772970332° = 54°50'50″ = 0.9577265919 rad
Angle ∠ C = γ = 92.12325513621° = 92°7'21″ = 1.60878418366 rad

Height: ha = 8.99438250422
Height: hb = 5.99658833614
Height: hc = 4.90657227503

Median: ma = 9.59216630466
Median: mb = 7.63221687612
Median: mc = 5.31550729064

Inradius: r = 2.07554980867
Circumradius: R = 5.50437761762

Vertex coordinates: A[11; 0] B[0; 0] C[3.45545454545; 4.90657227503]
Centroid: CG[4.81881818182; 1.63552409168]
Coordinates of the circumscribed circle: U[5.5; -0.20438435621]
Coordinates of the inscribed circle: I[4; 2.07554980867]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.9769848395° = 146°58'11″ = 0.57664848979 rad
∠ B' = β' = 125.1532702967° = 125°9'10″ = 0.9577265919 rad
∠ C' = γ' = 87.87774486379° = 87°52'39″ = 1.60878418366 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 = 6 ; ; b = 9 ; ; c = 11 ; ;

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

p = a+b+c = 6+9+11 = 26 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 26 }{ 2 } = 13 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13 * (13-6)(13-9)(13-11) } ; ; T = sqrt{ 728 } = 26.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 26.98 }{ 6 } = 8.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 26.98 }{ 9 } = 6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 26.98 }{ 11 } = 4.91 ; ;

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{ 6**2-9**2-11**2 }{ 2 * 9 * 11 } ) = 33° 1'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-6**2-11**2 }{ 2 * 6 * 11 } ) = 54° 50'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-6**2-9**2 }{ 2 * 9 * 6 } ) = 92° 7'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 26.98 }{ 13 } = 2.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 33° 1'49" } = 5.5 ; ;




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