14 14 19 triangle

Acute isosceles triangle.

Sides: a = 14   b = 14   c = 19

Area: T = 97.69330780557
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 47.26878899574° = 47°16'4″ = 0.82549803102 rad
Angle ∠ B = β = 47.26878899574° = 47°16'4″ = 0.82549803102 rad
Angle ∠ C = γ = 85.46442200852° = 85°27'51″ = 1.49216320331 rad

Height: ha = 13.9566154008
Height: hb = 13.9566154008
Height: hc = 10.28334819006

Median: ma = 15.14992574075
Median: mb = 15.14992574075
Median: mc = 10.28334819006

Inradius: r = 4.15771522577
Circumradius: R = 9.53298461112

Vertex coordinates: A[19; 0] B[0; 0] C[9.5; 10.28334819006]
Centroid: CG[9.5; 3.42878273002]
Coordinates of the circumscribed circle: U[9.5; 0.75436357894]
Coordinates of the inscribed circle: I[9.5; 4.15771522577]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.7322110043° = 132°43'56″ = 0.82549803102 rad
∠ B' = β' = 132.7322110043° = 132°43'56″ = 0.82549803102 rad
∠ C' = γ' = 94.53657799148° = 94°32'9″ = 1.49216320331 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 = 14 ; ; c = 19 ; ;

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

p = a+b+c = 14+14+19 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-14)(23.5-14)(23.5-19) } ; ; T = sqrt{ 9543.94 } = 97.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 97.69 }{ 14 } = 13.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 97.69 }{ 14 } = 13.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 97.69 }{ 19 } = 10.28 ; ;

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**2-14**2-19**2 }{ 2 * 14 * 19 } ) = 47° 16'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-14**2-19**2 }{ 2 * 14 * 19 } ) = 47° 16'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-14**2-14**2 }{ 2 * 14 * 14 } ) = 85° 27'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 97.69 }{ 23.5 } = 4.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 47° 16'4" } = 9.53 ; ;




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