8 13 17 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 13   c = 17

Area: T = 50.08799361022
Perimeter: p = 38
Semiperimeter: s = 19

Angle ∠ A = α = 26.95499559276° = 26°57' = 0.47703654642 rad
Angle ∠ B = β = 47.43215457967° = 47°25'54″ = 0.82878366435 rad
Angle ∠ C = γ = 105.6188498276° = 105°37'7″ = 1.84333905459 rad

Height: ha = 12.52199840255
Height: hb = 7.70546055542
Height: hc = 5.89217571885

Median: ma = 14.59545195193
Median: mb = 11.58766302263
Median: mc = 6.65220673478

Inradius: r = 2.63657861106
Circumradius: R = 8.82658898553

Vertex coordinates: A[17; 0] B[0; 0] C[5.41217647059; 5.89217571885]
Centroid: CG[7.47105882353; 1.96439190628]
Coordinates of the circumscribed circle: U[8.5; -2.37662011149]
Coordinates of the inscribed circle: I[6; 2.63657861106]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.0550044072° = 153°3' = 0.47703654642 rad
∠ B' = β' = 132.5688454203° = 132°34'6″ = 0.82878366435 rad
∠ C' = γ' = 74.38215017244° = 74°22'53″ = 1.84333905459 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 = 8 ; ; b = 13 ; ; c = 17 ; ;

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

p = a+b+c = 8+13+17 = 38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 38 }{ 2 } = 19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 19 * (19-8)(19-13)(19-17) } ; ; T = sqrt{ 2508 } = 50.08 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 50.08 }{ 8 } = 12.52 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 50.08 }{ 13 } = 7.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 50.08 }{ 17 } = 5.89 ; ;

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{ 8**2-13**2-17**2 }{ 2 * 13 * 17 } ) = 26° 57' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 13**2-8**2-17**2 }{ 2 * 8 * 17 } ) = 47° 25'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-8**2-13**2 }{ 2 * 13 * 8 } ) = 105° 37'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 50.08 }{ 19 } = 2.64 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 26° 57' } = 8.83 ; ;




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