11 26 27 triangle

Acute scalene triangle.

Sides: a = 11   b = 26   c = 27

Area: T = 141.9865914794
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 23.86109433465° = 23°51'39″ = 0.4166452024 rad
Angle ∠ B = β = 72.96765898339° = 72°58' = 1.27435072366 rad
Angle ∠ C = γ = 83.17224668196° = 83°10'21″ = 1.4521633393 rad

Height: ha = 25.81656208717
Height: hb = 10.92219934457
Height: hc = 10.517747517

Median: ma = 25.92877843249
Median: mb = 16
Median: mc = 14.70554411699

Inradius: r = 4.43770598373
Circumradius: R = 13.59664190729

Vertex coordinates: A[27; 0] B[0; 0] C[3.22222222222; 10.517747517]
Centroid: CG[10.07440740741; 3.50658250567]
Coordinates of the circumscribed circle: U[13.5; 1.61663575122]
Coordinates of the inscribed circle: I[6; 4.43770598373]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.1399056653° = 156°8'21″ = 0.4166452024 rad
∠ B' = β' = 107.0333410166° = 107°2' = 1.27435072366 rad
∠ C' = γ' = 96.82875331804° = 96°49'39″ = 1.4521633393 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 = 26 ; ; c = 27 ; ;

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

p = a+b+c = 11+26+27 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-11)(32-26)(32-27) } ; ; T = sqrt{ 20160 } = 141.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 141.99 }{ 11 } = 25.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 141.99 }{ 26 } = 10.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 141.99 }{ 27 } = 10.52 ; ;

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**2-26**2-27**2 }{ 2 * 26 * 27 } ) = 23° 51'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-11**2-27**2 }{ 2 * 11 * 27 } ) = 72° 58' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-11**2-26**2 }{ 2 * 26 * 11 } ) = 83° 10'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 141.99 }{ 32 } = 4.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 23° 51'39" } = 13.6 ; ;




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