6 9 14 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 9   c = 14

Area: T = 18.41102552943
Perimeter: p = 29
Semiperimeter: s = 14.5

Angle ∠ A = α = 16.9911286937° = 16°59'29″ = 0.29765539012 rad
Angle ∠ B = β = 25.99879769925° = 25°59'53″ = 0.45437502974 rad
Angle ∠ C = γ = 137.0110736071° = 137°39″ = 2.3911288455 rad

Height: ha = 6.13767517648
Height: hb = 4.09111678432
Height: hc = 2.63300364706

Median: ma = 11.38798066767
Median: mb = 9.78551928954
Median: mc = 3.08222070015

Inradius: r = 1.27696727789
Circumradius: R = 10.26660173354

Vertex coordinates: A[14; 0] B[0; 0] C[5.39328571429; 2.63300364706]
Centroid: CG[6.46442857143; 0.87766788235]
Coordinates of the circumscribed circle: U[7; -7.50994015694]
Coordinates of the inscribed circle: I[5.5; 1.27696727789]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.0098713063° = 163°31″ = 0.29765539012 rad
∠ B' = β' = 154.0022023008° = 154°7″ = 0.45437502974 rad
∠ C' = γ' = 42.98992639295° = 42°59'21″ = 2.3911288455 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 = 9 ; ; c = 14 ; ;

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

p = a+b+c = 6+9+14 = 29 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29 }{ 2 } = 14.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.5 * (14.5-6)(14.5-9)(14.5-14) } ; ; T = sqrt{ 338.94 } = 18.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18.41 }{ 6 } = 6.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18.41 }{ 9 } = 4.09 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18.41 }{ 14 } = 2.63 ; ;

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**2-9**2-14**2 }{ 2 * 9 * 14 } ) = 16° 59'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-6**2-14**2 }{ 2 * 6 * 14 } ) = 25° 59'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-6**2-9**2 }{ 2 * 9 * 6 } ) = 137° 39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18.41 }{ 14.5 } = 1.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 16° 59'29" } = 10.27 ; ;




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