6 9 13 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 9   c = 13

Area: T = 23.66443191324
Perimeter: p = 28
Semiperimeter: s = 14

Angle ∠ A = α = 23.86109433465° = 23°51'39″ = 0.4166452024 rad
Angle ∠ B = β = 37.35768519729° = 37°21'25″ = 0.65220000651 rad
Angle ∠ C = γ = 118.7822204681° = 118°46'56″ = 2.07331405645 rad

Height: ha = 7.88881063775
Height: hb = 5.2598737585
Height: hc = 3.64106644819

Median: ma = 10.77703296143
Median: mb = 9.06991785736
Median: mc = 4.03111288741

Inradius: r = 1.69903085095
Circumradius: R = 7.41662285852

Vertex coordinates: A[13; 0] B[0; 0] C[4.76992307692; 3.64106644819]
Centroid: CG[5.92330769231; 1.21435548273]
Coordinates of the circumscribed circle: U[6.5; -3.57107767262]
Coordinates of the inscribed circle: I[5; 1.69903085095]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.1399056653° = 156°8'21″ = 0.4166452024 rad
∠ B' = β' = 142.6433148027° = 142°38'35″ = 0.65220000651 rad
∠ C' = γ' = 61.21877953194° = 61°13'4″ = 2.07331405645 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 = 13 ; ;

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

p = a+b+c = 6+9+13 = 28 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 28 }{ 2 } = 14 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14 * (14-6)(14-9)(14-13) } ; ; T = sqrt{ 560 } = 23.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 23.66 }{ 6 } = 7.89 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 23.66 }{ 9 } = 5.26 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 23.66 }{ 13 } = 3.64 ; ;

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**2-13**2 }{ 2 * 9 * 13 } ) = 23° 51'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9**2-6**2-13**2 }{ 2 * 6 * 13 } ) = 37° 21'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-6**2-9**2 }{ 2 * 9 * 6 } ) = 118° 46'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 23.66 }{ 14 } = 1.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 23° 51'39" } = 7.42 ; ;




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