5 18 22 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 18   c = 22

Area: T = 29.76547022495
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 8.64658643504° = 8°38'45″ = 0.15108987996 rad
Angle ∠ B = β = 32.76437577589° = 32°45'50″ = 0.57218354482 rad
Angle ∠ C = γ = 138.5990377891° = 138°35'25″ = 2.41988584058 rad

Height: ha = 11.90658808998
Height: hb = 3.30771891388
Height: hc = 2.70658820227

Median: ma = 19.94436706752
Median: mb = 13.17219398723
Median: mc = 7.31443694192

Inradius: r = 1.32328756555
Circumradius: R = 16.63304368124

Vertex coordinates: A[22; 0] B[0; 0] C[4.20545454545; 2.70658820227]
Centroid: CG[8.73548484848; 0.90219606742]
Coordinates of the circumscribed circle: U[11; -12.47328276093]
Coordinates of the inscribed circle: I[4.5; 1.32328756555]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.354413565° = 171°21'15″ = 0.15108987996 rad
∠ B' = β' = 147.2366242241° = 147°14'10″ = 0.57218354482 rad
∠ C' = γ' = 41.41096221093° = 41°24'35″ = 2.41988584058 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 = 18 ; ; c = 22 ; ;

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

p = a+b+c = 5+18+22 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-5)(22.5-18)(22.5-22) } ; ; T = sqrt{ 885.94 } = 29.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 29.76 }{ 5 } = 11.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 29.76 }{ 18 } = 3.31 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 29.76 }{ 22 } = 2.71 ; ;

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**2-18**2-22**2 }{ 2 * 18 * 22 } ) = 8° 38'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-5**2-22**2 }{ 2 * 5 * 22 } ) = 32° 45'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-5**2-18**2 }{ 2 * 18 * 5 } ) = 138° 35'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 29.76 }{ 22.5 } = 1.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 8° 38'45" } = 16.63 ; ;




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