11.5 13.7 12.2 triangle

Acute scalene triangle.

Sides: a = 11.5   b = 13.7   c = 12.2

Area: T = 66.15498299318
Perimeter: p = 37.4
Semiperimeter: s = 18.7

Angle ∠ A = α = 52.33105942326° = 52°19'50″ = 0.91333411689 rad
Angle ∠ B = β = 70.55876536542° = 70°33'28″ = 1.23114633687 rad
Angle ∠ C = γ = 57.11217521133° = 57°6'42″ = 0.9976788116 rad

Height: ha = 11.5044318249
Height: hb = 9.65769094791
Height: hc = 10.8444234415

Median: ma = 11.62876609858
Median: mb = 9.67658720537
Median: mc = 11.08797111876

Inradius: r = 3.53774240605
Circumradius: R = 7.26442288045

Vertex coordinates: A[12.2; 0] B[0; 0] C[3.82878688525; 10.8444234415]
Centroid: CG[5.34326229508; 3.6154744805]
Coordinates of the circumscribed circle: U[6.1; 3.94444923784]
Coordinates of the inscribed circle: I[5; 3.53774240605]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.6699405767° = 127°40'10″ = 0.91333411689 rad
∠ B' = β' = 109.4422346346° = 109°26'32″ = 1.23114633687 rad
∠ C' = γ' = 122.8888247887° = 122°53'18″ = 0.9976788116 rad

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How did we calculate this triangle?

a = 11.5 ; ; b = 13.7 ; ; c = 12.2 ; ;

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

p = a+b+c = 11.5+13.7+12.2 = 37.4 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37.4 }{ 2 } = 18.7 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.7 * (18.7-11.5)(18.7-13.7)(18.7-12.2) } ; ; T = sqrt{ 4375.8 } = 66.15 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 66.15 }{ 11.5 } = 11.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 66.15 }{ 13.7 } = 9.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 66.15 }{ 12.2 } = 10.84 ; ;

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{ 11.5**2-13.7**2-12.2**2 }{ 2 * 13.7 * 12.2 } ) = 52° 19'50" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13.7**2-11.5**2-12.2**2 }{ 2 * 11.5 * 12.2 } ) = 70° 33'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12.2**2-11.5**2-13.7**2 }{ 2 * 13.7 * 11.5 } ) = 57° 6'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 66.15 }{ 18.7 } = 3.54 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11.5 }{ 2 * sin 52° 19'50" } = 7.26 ; ;




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