3 9 11 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 9   c = 11

Area: T = 11.05438454847
Perimeter: p = 23
Semiperimeter: s = 11.5

Angle ∠ A = α = 12.90435205392° = 12°54'13″ = 0.22552089185 rad
Angle ∠ B = β = 42.06216646665° = 42°3'42″ = 0.73441145373 rad
Angle ∠ C = γ = 125.0354814794° = 125°2'5″ = 2.18222691978 rad

Height: ha = 7.36992303231
Height: hb = 2.45664101077
Height: hc = 2.01097900881

Median: ma = 9.93773034572
Median: mb = 6.69895440801
Median: mc = 3.84105728739

Inradius: r = 0.96112039552
Circumradius: R = 6.71771194045

Vertex coordinates: A[11; 0] B[0; 0] C[2.22772727273; 2.01097900881]
Centroid: CG[4.40990909091; 0.67699300294]
Coordinates of the circumscribed circle: U[5.5; -3.85661241026]
Coordinates of the inscribed circle: I[2.5; 0.96112039552]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.0966479461° = 167°5'47″ = 0.22552089185 rad
∠ B' = β' = 137.9388335334° = 137°56'18″ = 0.73441145373 rad
∠ C' = γ' = 54.96551852057° = 54°57'55″ = 2.18222691978 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 = 3 ; ; b = 9 ; ; c = 11 ; ;

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

p = a+b+c = 3+9+11 = 23 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 23 }{ 2 } = 11.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.5 * (11.5-3)(11.5-9)(11.5-11) } ; ; T = sqrt{ 122.19 } = 11.05 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11.05 }{ 3 } = 7.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11.05 }{ 9 } = 2.46 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11.05 }{ 11 } = 2.01 ; ;

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{ 3**2-9**2-11**2 }{ 2 * 9 * 11 } ) = 12° 54'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-3**2-11**2 }{ 2 * 3 * 11 } ) = 42° 3'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-3**2-9**2 }{ 2 * 9 * 3 } ) = 125° 2'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11.05 }{ 11.5 } = 0.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 12° 54'13" } = 6.72 ; ;




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