10 18 26 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 18   c = 26

Area: T = 64.27328558569
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 15.94223686056° = 15°56'33″ = 0.27882468227 rad
Angle ∠ B = β = 29.63106273936° = 29°37'50″ = 0.51771520074 rad
Angle ∠ C = γ = 134.4277004001° = 134°25'37″ = 2.34661938234 rad

Height: ha = 12.85545711714
Height: hb = 7.14114284285
Height: hc = 4.94440658351

Median: ma = 21.79444947177
Median: mb = 17.52114154679
Median: mc = 6.55774385243

Inradius: r = 2.38804761428
Circumradius: R = 18.20436410924

Vertex coordinates: A[26; 0] B[0; 0] C[8.69223076923; 4.94440658351]
Centroid: CG[11.56441025641; 1.6488021945]
Coordinates of the circumscribed circle: U[13; -12.74325487647]
Coordinates of the inscribed circle: I[9; 2.38804761428]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.0587631394° = 164°3'27″ = 0.27882468227 rad
∠ B' = β' = 150.3699372606° = 150°22'10″ = 0.51771520074 rad
∠ C' = γ' = 45.57329959992° = 45°34'23″ = 2.34661938234 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 = 10 ; ; b = 18 ; ; c = 26 ; ;

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

p = a+b+c = 10+18+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 * (27-10)(27-18)(27-26) } ; ; T = sqrt{ 4131 } = 64.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 64.27 }{ 10 } = 12.85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 64.27 }{ 18 } = 7.14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 64.27 }{ 26 } = 4.94 ; ;

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{ 10**2-18**2-26**2 }{ 2 * 18 * 26 } ) = 15° 56'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-10**2-26**2 }{ 2 * 10 * 26 } ) = 29° 37'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-10**2-18**2 }{ 2 * 18 * 10 } ) = 134° 25'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 64.27 }{ 27 } = 2.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 15° 56'33" } = 18.2 ; ;




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