13 18 26 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 18   c = 26

Area: T = 107.6844434808
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 27.39993615864° = 27°23'58″ = 0.47882090726 rad
Angle ∠ B = β = 39.58223055699° = 39°34'56″ = 0.69108415577 rad
Angle ∠ C = γ = 113.0188332844° = 113°1'6″ = 1.97325420232 rad

Height: ha = 16.56768361244
Height: hb = 11.96549372009
Height: hc = 8.28334180622

Median: ma = 21.39550928953
Median: mb = 18.48797186126
Median: mc = 8.80334084308

Inradius: r = 3.77884012213
Circumradius: R = 14.12546040127

Vertex coordinates: A[26; 0] B[0; 0] C[10.01992307692; 8.28334180622]
Centroid: CG[12.00664102564; 2.76111393541]
Coordinates of the circumscribed circle: U[13; -5.52330823383]
Coordinates of the inscribed circle: I[10.5; 3.77884012213]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.6010638414° = 152°36'2″ = 0.47882090726 rad
∠ B' = β' = 140.418769443° = 140°25'4″ = 0.69108415577 rad
∠ C' = γ' = 66.98216671563° = 66°58'54″ = 1.97325420232 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 = 13 ; ; b = 18 ; ; c = 26 ; ;

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

p = a+b+c = 13+18+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 * (28.5-13)(28.5-18)(28.5-26) } ; ; T = sqrt{ 11595.94 } = 107.68 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 107.68 }{ 13 } = 16.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 107.68 }{ 18 } = 11.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 107.68 }{ 26 } = 8.28 ; ;

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{ 13**2-18**2-26**2 }{ 2 * 18 * 26 } ) = 27° 23'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-13**2-26**2 }{ 2 * 13 * 26 } ) = 39° 34'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-13**2-18**2 }{ 2 * 18 * 13 } ) = 113° 1'6" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 107.68 }{ 28.5 } = 3.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 27° 23'58" } = 14.12 ; ;




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