6 18 22 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 18   c = 22

Area: T = 44.21553819389
Perimeter: p = 46
Semiperimeter: s = 23

Angle ∠ A = α = 12.90435205392° = 12°54'13″ = 0.22552089185 rad
Angle ∠ B = β = 42.06216646665° = 42°3'42″ = 0.73441145373 rad
Angle ∠ C = γ = 125.0354814794° = 125°2'5″ = 2.18222691978 rad

Height: ha = 14.73884606463
Height: hb = 4.91328202154
Height: hc = 4.02195801763

Median: ma = 19.87546069144
Median: mb = 13.37990881603
Median: mc = 7.68111457479

Inradius: r = 1.92224079104
Circumradius: R = 13.4344238809

Vertex coordinates: A[22; 0] B[0; 0] C[4.45545454545; 4.02195801763]
Centroid: CG[8.81881818182; 1.34398600588]
Coordinates of the circumscribed circle: U[11; -7.71222482052]
Coordinates of the inscribed circle: I[5; 1.92224079104]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.0966479461° = 167°5'47″ = 0.22552089185 rad
∠ B' = β' = 137.9388335334° = 137°56'18″ = 0.73441145373 rad
∠ C' = γ' = 54.96551852057° = 54°57'55″ = 2.18222691978 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 = 6 ; ; b = 18 ; ; c = 22 ; ;

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

p = a+b+c = 6+18+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 * (23-6)(23-18)(23-22) } ; ; T = sqrt{ 1955 } = 44.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.22 }{ 6 } = 14.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.22 }{ 18 } = 4.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.22 }{ 22 } = 4.02 ; ;

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{ 6**2-18**2-22**2 }{ 2 * 18 * 22 } ) = 12° 54'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-6**2-22**2 }{ 2 * 6 * 22 } ) = 42° 3'42" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-6**2-18**2 }{ 2 * 18 * 6 } ) = 125° 2'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.22 }{ 23 } = 1.92 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 12° 54'13" } = 13.43 ; ;




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