7 9 11 triangle

Acute scalene triangle.

Sides: a = 7   b = 9   c = 11

Area: T = 31.42195400985
Perimeter: p = 27
Semiperimeter: s = 13.5

Angle ∠ A = α = 39.40105687537° = 39°24'2″ = 0.68876696519 rad
Angle ∠ B = β = 54.69554750044° = 54°41'44″ = 0.95546161248 rad
Angle ∠ C = γ = 85.90439562418° = 85°54'14″ = 1.49993068769 rad

Height: ha = 8.97770114567
Height: hb = 6.98221200219
Height: hc = 5.71326436543

Median: ma = 9.42107218407
Median: mb = 8.04767384697
Median: mc = 5.89549130613

Inradius: r = 2.32773733406
Circumradius: R = 5.51440845301

Vertex coordinates: A[11; 0] B[0; 0] C[4.04554545455; 5.71326436543]
Centroid: CG[5.01551515152; 1.90442145514]
Coordinates of the circumscribed circle: U[5.5; 0.39438631807]
Coordinates of the inscribed circle: I[4.5; 2.32773733406]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.5999431246° = 140°35'58″ = 0.68876696519 rad
∠ B' = β' = 125.3054524996° = 125°18'16″ = 0.95546161248 rad
∠ C' = γ' = 94.09660437582° = 94°5'46″ = 1.49993068769 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 = 7 ; ; b = 9 ; ; c = 11 ; ;

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

p = a+b+c = 7+9+11 = 27 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27 }{ 2 } = 13.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.5 * (13.5-7)(13.5-9)(13.5-11) } ; ; T = sqrt{ 987.19 } = 31.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 31.42 }{ 7 } = 8.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 31.42 }{ 9 } = 6.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 31.42 }{ 11 } = 5.71 ; ;

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{ 7**2-9**2-11**2 }{ 2 * 9 * 11 } ) = 39° 24'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-7**2-11**2 }{ 2 * 7 * 11 } ) = 54° 41'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 11**2-7**2-9**2 }{ 2 * 9 * 7 } ) = 85° 54'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 31.42 }{ 13.5 } = 2.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 39° 24'2" } = 5.51 ; ;




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