9 11 18 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 11   c = 18

Area: T = 38.98771773792
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 23.192176951° = 23°11'30″ = 0.40547727373 rad
Angle ∠ B = β = 28.77218565328° = 28°46'19″ = 0.50221636284 rad
Angle ∠ C = γ = 128.0366373957° = 128°2'11″ = 2.23546562879 rad

Height: ha = 8.66438171954
Height: hb = 7.08985777053
Height: hc = 4.33219085977

Median: ma = 14.22114626533
Median: mb = 13.12444047484
Median: mc = 4.4722135955

Inradius: r = 2.05219567042
Circumradius: R = 11.42768338963

Vertex coordinates: A[18; 0] B[0; 0] C[7.88988888889; 4.33219085977]
Centroid: CG[8.63296296296; 1.44439695326]
Coordinates of the circumscribed circle: U[9; -7.04107764412]
Coordinates of the inscribed circle: I[8; 2.05219567042]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.808823049° = 156°48'30″ = 0.40547727373 rad
∠ B' = β' = 151.2288143467° = 151°13'41″ = 0.50221636284 rad
∠ C' = γ' = 51.96436260429° = 51°57'49″ = 2.23546562879 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 = 11 ; ; c = 18 ; ;

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

p = a+b+c = 9+11+18 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-9)(19-11)(19-18) } ; ; T = sqrt{ 1520 } = 38.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 38.99 }{ 9 } = 8.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 38.99 }{ 11 } = 7.09 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 38.99 }{ 18 } = 4.33 ; ;

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**2-11**2-18**2 }{ 2 * 11 * 18 } ) = 23° 11'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-9**2-18**2 }{ 2 * 9 * 18 } ) = 28° 46'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-9**2-11**2 }{ 2 * 11 * 9 } ) = 128° 2'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 38.99 }{ 19 } = 2.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 23° 11'30" } = 11.43 ; ;




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