9 10 14 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 10   c = 14

Area: T = 44.84334777866
Perimeter: p = 33
Semiperimeter: s = 16.5

Angle ∠ A = α = 39.83881498056° = 39°50'17″ = 0.6955306882 rad
Angle ∠ B = β = 45.38216583472° = 45°22'54″ = 0.79220593582 rad
Angle ∠ C = γ = 94.78801918472° = 94°46'49″ = 1.65442264134 rad

Height: ha = 9.96552172859
Height: hb = 8.96986955573
Height: hc = 6.40662111124

Median: ma = 11.30326545555
Median: mb = 10.65436378763
Median: mc = 6.44220493634

Inradius: r = 2.71877865325
Circumradius: R = 7.02444328841

Vertex coordinates: A[14; 0] B[0; 0] C[6.32114285714; 6.40662111124]
Centroid: CG[6.77438095238; 2.13554037041]
Coordinates of the circumscribed circle: U[7; -0.5855369407]
Coordinates of the inscribed circle: I[6.5; 2.71877865325]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.1621850194° = 140°9'43″ = 0.6955306882 rad
∠ B' = β' = 134.6188341653° = 134°37'6″ = 0.79220593582 rad
∠ C' = γ' = 85.22198081528° = 85°13'11″ = 1.65442264134 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 = 10 ; ; c = 14 ; ;

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

p = a+b+c = 9+10+14 = 33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33 }{ 2 } = 16.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.5 * (16.5-9)(16.5-10)(16.5-14) } ; ; T = sqrt{ 2010.94 } = 44.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 44.84 }{ 9 } = 9.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 44.84 }{ 10 } = 8.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 44.84 }{ 14 } = 6.41 ; ;

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**2-10**2-14**2 }{ 2 * 10 * 14 } ) = 39° 50'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-9**2-14**2 }{ 2 * 9 * 14 } ) = 45° 22'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-9**2-10**2 }{ 2 * 10 * 9 } ) = 94° 46'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 44.84 }{ 16.5 } = 2.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 39° 50'17" } = 7.02 ; ;




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