13 19 26 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 19   c = 26

Area: T = 117.983304963
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 28.53329559873° = 28°31'59″ = 0.49879940273 rad
Angle ∠ B = β = 44.27767297027° = 44°16'36″ = 0.77327747153 rad
Angle ∠ C = γ = 107.199031431° = 107°11'25″ = 1.8710823911 rad

Height: ha = 18.15112384046
Height: hb = 12.41992683821
Height: hc = 9.07656192023

Median: ma = 21.82331528428
Median: mb = 18.22877261336
Median: mc = 9.79879589711

Inradius: r = 4.06883810217
Circumradius: R = 13.60878869383

Vertex coordinates: A[26; 0] B[0; 0] C[9.30876923077; 9.07656192023]
Centroid: CG[11.76992307692; 3.02552064008]
Coordinates of the circumscribed circle: U[13; -4.02217641559]
Coordinates of the inscribed circle: I[10; 4.06883810217]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.4677044013° = 151°28'1″ = 0.49879940273 rad
∠ B' = β' = 135.7233270297° = 135°43'24″ = 0.77327747153 rad
∠ C' = γ' = 72.81096856901° = 72°48'35″ = 1.8710823911 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 = 19 ; ; c = 26 ; ;

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

p = a+b+c = 13+19+26 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-13)(29-19)(29-26) } ; ; T = sqrt{ 13920 } = 117.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 117.98 }{ 13 } = 18.15 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 117.98 }{ 19 } = 12.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 117.98 }{ 26 } = 9.08 ; ;

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**2-19**2-26**2 }{ 2 * 19 * 26 } ) = 28° 31'59" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-13**2-26**2 }{ 2 * 13 * 26 } ) = 44° 16'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-13**2-19**2 }{ 2 * 19 * 13 } ) = 107° 11'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 117.98 }{ 29 } = 4.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 28° 31'59" } = 13.61 ; ;




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