9 13 18 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 13   c = 18

Area: T = 55.4987747702
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 28.31663682245° = 28°18'59″ = 0.49442138577 rad
Angle ∠ B = β = 43.24879853748° = 43°14'53″ = 0.75548197396 rad
Angle ∠ C = γ = 108.4365646401° = 108°26'8″ = 1.89325590562 rad

Height: ha = 12.33328328227
Height: hb = 8.53881150311
Height: hc = 6.16664164113

Median: ma = 15.04216089565
Median: mb = 12.65989889012
Median: mc = 6.63332495807

Inradius: r = 2.77548873851
Circumradius: R = 9.48768714822

Vertex coordinates: A[18; 0] B[0; 0] C[6.55655555556; 6.16664164113]
Centroid: CG[8.18551851852; 2.05554721371]
Coordinates of the circumscribed circle: U[9; -33.0001217508]
Coordinates of the inscribed circle: I[7; 2.77548873851]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.6843631775° = 151°41'1″ = 0.49442138577 rad
∠ B' = β' = 136.7522014625° = 136°45'7″ = 0.75548197396 rad
∠ C' = γ' = 71.56443535993° = 71°33'52″ = 1.89325590562 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 = 9 ; ; b = 13 ; ; c = 18 ; ;

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

p = a+b+c = 9+13+18 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-9)(20-13)(20-18) } ; ; T = sqrt{ 3080 } = 55.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 55.5 }{ 9 } = 12.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 55.5 }{ 13 } = 8.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 55.5 }{ 18 } = 6.17 ; ;

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{ 9**2-13**2-18**2 }{ 2 * 13 * 18 } ) = 28° 18'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-9**2-18**2 }{ 2 * 9 * 18 } ) = 43° 14'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-9**2-13**2 }{ 2 * 13 * 9 } ) = 108° 26'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 55.5 }{ 20 } = 2.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 28° 18'59" } = 9.49 ; ;




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