9 19 26 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 19   c = 26

Area: T = 62.35438290725
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 14.62222213888° = 14°37'20″ = 0.25552059072 rad
Angle ∠ B = β = 32.2044227504° = 32°12'15″ = 0.5622069803 rad
Angle ∠ C = γ = 133.1743551107° = 133°10'25″ = 2.32443169434 rad

Height: ha = 13.85664064606
Height: hb = 6.5643560955
Height: hc = 4.79664483902

Median: ma = 22.32215142855
Median: mb = 16.97879268463
Median: mc = 7.21111025509

Inradius: r = 2.30994010768
Circumradius: R = 17.82656895612

Vertex coordinates: A[26; 0] B[0; 0] C[7.61553846154; 4.79664483902]
Centroid: CG[11.20551282051; 1.59988161301]
Coordinates of the circumscribed circle: U[13; -12.19765244366]
Coordinates of the inscribed circle: I[8; 2.30994010768]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.3787778611° = 165°22'40″ = 0.25552059072 rad
∠ B' = β' = 147.7965772496° = 147°47'45″ = 0.5622069803 rad
∠ C' = γ' = 46.82664488927° = 46°49'35″ = 2.32443169434 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 = 9 ; ; b = 19 ; ; c = 26 ; ;

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

p = a+b+c = 9+19+26 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-9)(27-19)(27-26) } ; ; T = sqrt{ 3888 } = 62.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 62.35 }{ 9 } = 13.86 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 62.35 }{ 19 } = 6.56 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 62.35 }{ 26 } = 4.8 ; ;

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{ 9**2-19**2-26**2 }{ 2 * 19 * 26 } ) = 14° 37'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-9**2-26**2 }{ 2 * 9 * 26 } ) = 32° 12'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-9**2-19**2 }{ 2 * 19 * 9 } ) = 133° 10'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 62.35 }{ 27 } = 2.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 14° 37'20" } = 17.83 ; ;




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