16 18 19 triangle

Acute scalene triangle.

Sides: a = 16   b = 18   c = 19

Area: T = 133.1865725587
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 51.15766718327° = 51°9'24″ = 0.89328523578 rad
Angle ∠ B = β = 61.19899160656° = 61°11'24″ = 1.06879655044 rad
Angle ∠ C = γ = 67.65334121016° = 67°39'12″ = 1.18107747914 rad

Height: ha = 16.64882156983
Height: hb = 14.79884139541
Height: hc = 14.02195500617

Median: ma = 16.68883192683
Median: mb = 15.0833103129
Median: mc = 14.13332940251

Inradius: r = 5.02658764372
Circumradius: R = 10.27113710045

Vertex coordinates: A[19; 0] B[0; 0] C[7.71105263158; 14.02195500617]
Centroid: CG[8.90435087719; 4.67331833539]
Coordinates of the circumscribed circle: U[9.5; 3.90552608507]
Coordinates of the inscribed circle: I[8.5; 5.02658764372]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.8433328167° = 128°50'36″ = 0.89328523578 rad
∠ B' = β' = 118.8110083934° = 118°48'36″ = 1.06879655044 rad
∠ C' = γ' = 112.3476587898° = 112°20'48″ = 1.18107747914 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 = 16 ; ; b = 18 ; ; c = 19 ; ;

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

p = a+b+c = 16+18+19 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-16)(26.5-18)(26.5-19) } ; ; T = sqrt{ 17738.44 } = 133.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 133.19 }{ 16 } = 16.65 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 133.19 }{ 18 } = 14.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 133.19 }{ 19 } = 14.02 ; ;

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{ 16**2-18**2-19**2 }{ 2 * 18 * 19 } ) = 51° 9'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-16**2-19**2 }{ 2 * 16 * 19 } ) = 61° 11'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 19**2-16**2-18**2 }{ 2 * 18 * 16 } ) = 67° 39'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 133.19 }{ 26.5 } = 5.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 51° 9'24" } = 10.27 ; ;




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