14 20 30 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 20   c = 30

Area: T = 117.5765507654
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 23.07439180656° = 23°4'26″ = 0.40327158416 rad
Angle ∠ B = β = 34.048773237° = 34°2'52″ = 0.59442450327 rad
Angle ∠ C = γ = 122.8788349564° = 122°52'42″ = 2.14546317793 rad

Height: ha = 16.79765010934
Height: hb = 11.75875507654
Height: hc = 7.83883671769

Median: ma = 24.51553013443
Median: mb = 21.16660104885
Median: mc = 8.54440037453

Inradius: r = 3.67442346142
Circumradius: R = 17.86108627078

Vertex coordinates: A[30; 0] B[0; 0] C[11.6; 7.83883671769]
Centroid: CG[13.86766666667; 2.6132789059]
Coordinates of the circumscribed circle: U[15; -9.69658968985]
Coordinates of the inscribed circle: I[12; 3.67442346142]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.9266081934° = 156°55'34″ = 0.40327158416 rad
∠ B' = β' = 145.952226763° = 145°57'8″ = 0.59442450327 rad
∠ C' = γ' = 57.12216504356° = 57°7'18″ = 2.14546317793 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 = 14 ; ; b = 20 ; ; c = 30 ; ;

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

p = a+b+c = 14+20+30 = 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 * (32-14)(32-20)(32-30) } ; ; T = sqrt{ 13824 } = 117.58 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 117.58 }{ 14 } = 16.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 117.58 }{ 20 } = 11.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 117.58 }{ 30 } = 7.84 ; ;

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{ 14**2-20**2-30**2 }{ 2 * 20 * 30 } ) = 23° 4'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-14**2-30**2 }{ 2 * 14 * 30 } ) = 34° 2'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-14**2-20**2 }{ 2 * 20 * 14 } ) = 122° 52'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 117.58 }{ 32 } = 3.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 23° 4'26" } = 17.86 ; ;




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