9 14 18 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 14   c = 18

Area: T = 61.8954567613
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 29.42112427193° = 29°25'16″ = 0.51334975555 rad
Angle ∠ B = β = 49.83296961902° = 49°49'47″ = 0.87696922638 rad
Angle ∠ C = γ = 100.749906109° = 100°44'57″ = 1.75884028343 rad

Height: ha = 13.75443483584
Height: hb = 8.84220810876
Height: hc = 6.87771741792

Median: ma = 15.48438625672
Median: mb = 12.39895116934
Median: mc = 7.58328754441

Inradius: r = 3.01992472006
Circumradius: R = 9.16107393325

Vertex coordinates: A[18; 0] B[0; 0] C[5.80655555556; 6.87771741792]
Centroid: CG[7.93551851852; 2.29223913931]
Coordinates of the circumscribed circle: U[9; -1.70985505898]
Coordinates of the inscribed circle: I[6.5; 3.01992472006]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.5798757281° = 150°34'44″ = 0.51334975555 rad
∠ B' = β' = 130.177030381° = 130°10'13″ = 0.87696922638 rad
∠ C' = γ' = 79.25109389095° = 79°15'3″ = 1.75884028343 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 = 14 ; ; c = 18 ; ;

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

p = a+b+c = 9+14+18 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-9)(20.5-14)(20.5-18) } ; ; T = sqrt{ 3830.94 } = 61.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 61.89 }{ 9 } = 13.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 61.89 }{ 14 } = 8.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 61.89 }{ 18 } = 6.88 ; ;

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**2-14**2-18**2 }{ 2 * 14 * 18 } ) = 29° 25'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-9**2-18**2 }{ 2 * 9 * 18 } ) = 49° 49'47" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-9**2-14**2 }{ 2 * 14 * 9 } ) = 100° 44'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 61.89 }{ 20.5 } = 3.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 29° 25'16" } = 9.16 ; ;




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