11 22 26 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 22   c = 26

Area: T = 119.6911008434
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 24.74399242471° = 24°44'24″ = 0.43217931348 rad
Angle ∠ B = β = 56.82546760001° = 56°49'29″ = 0.99217776926 rad
Angle ∠ C = γ = 98.43553997528° = 98°26'7″ = 1.71880218262 rad

Height: ha = 21.76220015335
Height: hb = 10.88110007667
Height: hc = 9.20770006488

Median: ma = 23.44767481754
Median: mb = 16.6588331249
Median: mc = 11.55442200083

Inradius: r = 4.05773223198
Circumradius: R = 13.14221735064

Vertex coordinates: A[26; 0] B[0; 0] C[6.01992307692; 9.20770006488]
Centroid: CG[10.67330769231; 3.06990002163]
Coordinates of the circumscribed circle: U[13; -1.92878808243]
Coordinates of the inscribed circle: I[7.5; 4.05773223198]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.2660075753° = 155°15'36″ = 0.43217931348 rad
∠ B' = β' = 123.1755324° = 123°10'31″ = 0.99217776926 rad
∠ C' = γ' = 81.56546002472° = 81°33'53″ = 1.71880218262 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 = 11 ; ; b = 22 ; ; c = 26 ; ;

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

p = a+b+c = 11+22+26 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-11)(29.5-22)(29.5-26) } ; ; T = sqrt{ 14325.94 } = 119.69 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 119.69 }{ 11 } = 21.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 119.69 }{ 22 } = 10.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 119.69 }{ 26 } = 9.21 ; ;

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{ 11**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 24° 44'24" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-11**2-26**2 }{ 2 * 11 * 26 } ) = 56° 49'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-11**2-22**2 }{ 2 * 22 * 11 } ) = 98° 26'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 119.69 }{ 29.5 } = 4.06 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 24° 44'24" } = 13.14 ; ;




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