5 19 22 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 19   c = 22

Area: T = 40.69439798988
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 11.22876684821° = 11°13'40″ = 0.19659597823 rad
Angle ∠ B = β = 47.72220924012° = 47°43'20″ = 0.83329076383 rad
Angle ∠ C = γ = 121.0550239117° = 121°3'1″ = 2.11327252329 rad

Height: ha = 16.27875919595
Height: hb = 4.28435768314
Height: hc = 3.69994527181

Median: ma = 20.40222057631
Median: mb = 12.8166005618
Median: mc = 8.48552813742

Inradius: r = 1.76993034739
Circumradius: R = 12.84397370152

Vertex coordinates: A[22; 0] B[0; 0] C[3.36436363636; 3.69994527181]
Centroid: CG[8.45545454545; 1.2333150906]
Coordinates of the circumscribed circle: U[11; -6.62326011973]
Coordinates of the inscribed circle: I[4; 1.76993034739]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.7722331518° = 168°46'20″ = 0.19659597823 rad
∠ B' = β' = 132.2787907599° = 132°16'40″ = 0.83329076383 rad
∠ C' = γ' = 58.95497608832° = 58°56'59″ = 2.11327252329 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 = 5 ; ; b = 19 ; ; c = 22 ; ;

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

p = a+b+c = 5+19+22 = 46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46 }{ 2 } = 23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23 * (23-5)(23-19)(23-22) } ; ; T = sqrt{ 1656 } = 40.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 40.69 }{ 5 } = 16.28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 40.69 }{ 19 } = 4.28 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 40.69 }{ 22 } = 3.7 ; ;

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{ 5**2-19**2-22**2 }{ 2 * 19 * 22 } ) = 11° 13'40" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-5**2-22**2 }{ 2 * 5 * 22 } ) = 47° 43'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-5**2-19**2 }{ 2 * 19 * 5 } ) = 121° 3'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 40.69 }{ 23 } = 1.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 11° 13'40" } = 12.84 ; ;




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