8 23 26 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 23   c = 26

Area: T = 89.62994454964
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 17.44334308804° = 17°26'36″ = 0.30444453017 rad
Angle ∠ B = β = 59.52217304315° = 59°31'18″ = 1.03988501725 rad
Angle ∠ C = γ = 103.0354838688° = 103°2'5″ = 1.79882971794 rad

Height: ha = 22.40773613741
Height: hb = 7.79438648258
Height: hc = 6.89545727305

Median: ma = 24.21877620766
Median: mb = 15.41991439451
Median: mc = 11.29215897906

Inradius: r = 3.14548928244
Circumradius: R = 13.34438290662

Vertex coordinates: A[26; 0] B[0; 0] C[4.05876923077; 6.89545727305]
Centroid: CG[10.01992307692; 2.29881909102]
Coordinates of the circumscribed circle: U[13; -3.01096136209]
Coordinates of the inscribed circle: I[5.5; 3.14548928244]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.557656912° = 162°33'24″ = 0.30444453017 rad
∠ B' = β' = 120.4788269569° = 120°28'42″ = 1.03988501725 rad
∠ C' = γ' = 76.96551613118° = 76°57'55″ = 1.79882971794 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 = 23 ; ; c = 26 ; ;

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

p = a+b+c = 8+23+26 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-8)(28.5-23)(28.5-26) } ; ; T = sqrt{ 8033.44 } = 89.63 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 89.63 }{ 8 } = 22.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 89.63 }{ 23 } = 7.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 89.63 }{ 26 } = 6.89 ; ;

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**2-23**2-26**2 }{ 2 * 23 * 26 } ) = 17° 26'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-8**2-26**2 }{ 2 * 8 * 26 } ) = 59° 31'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-8**2-23**2 }{ 2 * 23 * 8 } ) = 103° 2'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 89.63 }{ 28.5 } = 3.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 17° 26'36" } = 13.34 ; ;




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