19 22 28 triangle

Acute scalene triangle.

Sides: a = 19   b = 22   c = 28

Area: T = 208.4432887861
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 42.59111780237° = 42°35'28″ = 0.74333562888 rad
Angle ∠ B = β = 51.59332135275° = 51°35'36″ = 0.99004714477 rad
Angle ∠ C = γ = 85.81656084488° = 85°48'56″ = 1.4987764917 rad

Height: ha = 21.9411356617
Height: hb = 18.94993534419
Height: hc = 14.88987777044

Median: ma = 23.31884476327
Median: mb = 21.24985293609
Median: mc = 15.05499169433

Inradius: r = 6.04218228366
Circumradius: R = 14.03774182589

Vertex coordinates: A[28; 0] B[0; 0] C[11.80435714286; 14.88987777044]
Centroid: CG[13.26878571429; 4.96329259015]
Coordinates of the circumscribed circle: U[14; 1.02442613801]
Coordinates of the inscribed circle: I[12.5; 6.04218228366]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.4098821976° = 137°24'32″ = 0.74333562888 rad
∠ B' = β' = 128.4076786473° = 128°24'24″ = 0.99004714477 rad
∠ C' = γ' = 94.18443915512° = 94°11'4″ = 1.4987764917 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 = 19 ; ; b = 22 ; ; c = 28 ; ;

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

p = a+b+c = 19+22+28 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-19)(34.5-22)(34.5-28) } ; ; T = sqrt{ 43448.44 } = 208.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 208.44 }{ 19 } = 21.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 208.44 }{ 22 } = 18.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 208.44 }{ 28 } = 14.89 ; ;

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{ 19**2-22**2-28**2 }{ 2 * 22 * 28 } ) = 42° 35'28" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-19**2-28**2 }{ 2 * 19 * 28 } ) = 51° 35'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-19**2-22**2 }{ 2 * 22 * 19 } ) = 85° 48'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 208.44 }{ 34.5 } = 6.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 19 }{ 2 * sin 42° 35'28" } = 14.04 ; ;




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