12 22 26 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 22   c = 26

Area: T = 131.4533413801
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 27.36330618223° = 27°21'47″ = 0.47875755222 rad
Angle ∠ B = β = 57.42110296072° = 57°25'16″ = 1.00221860265 rad
Angle ∠ C = γ = 95.21659085705° = 95°12'57″ = 1.66218311048 rad

Height: ha = 21.90989023002
Height: hb = 11.95503103456
Height: hc = 10.11218010616

Median: ma = 23.32438075794
Median: mb = 17
Median: mc = 12.04215945788

Inradius: r = 4.382178046
Circumradius: R = 13.05440542872

Vertex coordinates: A[26; 0] B[0; 0] C[6.46215384615; 10.11218010616]
Centroid: CG[10.82105128205; 3.37106003539]
Coordinates of the circumscribed circle: U[13; -1.18767322079]
Coordinates of the inscribed circle: I[8; 4.382178046]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.6376938178° = 152°38'13″ = 0.47875755222 rad
∠ B' = β' = 122.5798970393° = 122°34'44″ = 1.00221860265 rad
∠ C' = γ' = 84.78440914295° = 84°47'3″ = 1.66218311048 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 = 12 ; ; b = 22 ; ; c = 26 ; ;

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

p = a+b+c = 12+22+26 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-12)(30-22)(30-26) } ; ; T = sqrt{ 17280 } = 131.45 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 131.45 }{ 12 } = 21.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 131.45 }{ 22 } = 11.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 131.45 }{ 26 } = 10.11 ; ;

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{ 12**2-22**2-26**2 }{ 2 * 22 * 26 } ) = 27° 21'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-12**2-26**2 }{ 2 * 12 * 26 } ) = 57° 25'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-12**2-22**2 }{ 2 * 22 * 12 } ) = 95° 12'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 131.45 }{ 30 } = 4.38 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 27° 21'47" } = 13.05 ; ;




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