4 9 11 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 9   c = 11

Area: T = 16.97105627485
Perimeter: p = 24
Semiperimeter: s = 12

Angle ∠ A = α = 20.05499757242° = 20°3' = 0.35499380913 rad
Angle ∠ B = β = 50.47988036414° = 50°28'44″ = 0.8811021326 rad
Angle ∠ C = γ = 109.4711220634° = 109°28'16″ = 1.91106332362 rad

Height: ha = 8.48552813742
Height: hb = 3.77112361663
Height: hc = 3.08655568634

Median: ma = 9.84988578018
Median: mb = 6.94662219947
Median: mc = 4.27220018727

Inradius: r = 1.41442135624
Circumradius: R = 5.83436309448

Vertex coordinates: A[11; 0] B[0; 0] C[2.54554545455; 3.08655568634]
Centroid: CG[4.51551515152; 1.02985189545]
Coordinates of the circumscribed circle: U[5.5; -1.94545436483]
Coordinates of the inscribed circle: I[3; 1.41442135624]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.9550024276° = 159°57' = 0.35499380913 rad
∠ B' = β' = 129.5211196359° = 129°31'16″ = 0.8811021326 rad
∠ C' = γ' = 70.52987793655° = 70°31'44″ = 1.91106332362 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 = 4 ; ; b = 9 ; ; c = 11 ; ;

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

p = a+b+c = 4+9+11 = 24 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24 }{ 2 } = 12 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12 * (12-4)(12-9)(12-11) } ; ; T = sqrt{ 288 } = 16.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16.97 }{ 4 } = 8.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16.97 }{ 9 } = 3.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16.97 }{ 11 } = 3.09 ; ;

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{ 4**2-9**2-11**2 }{ 2 * 9 * 11 } ) = 20° 3' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-4**2-11**2 }{ 2 * 4 * 11 } ) = 50° 28'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-4**2-9**2 }{ 2 * 9 * 4 } ) = 109° 28'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16.97 }{ 12 } = 1.41 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 20° 3' } = 5.83 ; ;




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