6 8 13 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 8   c = 13

Area: T = 16.6866446596
Perimeter: p = 27
Semiperimeter: s = 13.5

Angle ∠ A = α = 18.71769506574° = 18°43'1″ = 0.32766724149 rad
Angle ∠ B = β = 25.33216750167° = 25°19'54″ = 0.44221211341 rad
Angle ∠ C = γ = 135.9511374326° = 135°57'5″ = 2.37327991046 rad

Height: ha = 5.56221488653
Height: hb = 4.1721611649
Height: hc = 2.56771456301

Median: ma = 10.36882206767
Median: mb = 9.30105376189
Median: mc = 2.78438821814

Inradius: r = 1.23660330812
Circumradius: R = 9.34989047595

Vertex coordinates: A[13; 0] B[0; 0] C[5.42330769231; 2.56771456301]
Centroid: CG[6.1411025641; 0.856571521]
Coordinates of the circumscribed circle: U[6.5; -6.72195252959]
Coordinates of the inscribed circle: I[5.5; 1.23660330812]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.2833049343° = 161°16'59″ = 0.32766724149 rad
∠ B' = β' = 154.6688324983° = 154°40'6″ = 0.44221211341 rad
∠ C' = γ' = 44.04986256741° = 44°2'55″ = 2.37327991046 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 = 8 ; ; c = 13 ; ;

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

p = a+b+c = 6+8+13 = 27 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 27 }{ 2 } = 13.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.5 * (13.5-6)(13.5-8)(13.5-13) } ; ; T = sqrt{ 278.44 } = 16.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16.69 }{ 6 } = 5.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16.69 }{ 8 } = 4.17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16.69 }{ 13 } = 2.57 ; ;

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**2-8**2-13**2 }{ 2 * 8 * 13 } ) = 18° 43'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8**2-6**2-13**2 }{ 2 * 6 * 13 } ) = 25° 19'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13**2-6**2-8**2 }{ 2 * 8 * 6 } ) = 135° 57'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16.69 }{ 13.5 } = 1.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 18° 43'1" } = 9.35 ; ;




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