12 26 26 triangle

Acute isosceles triangle.

Sides: a = 12   b = 26   c = 26

Area: T = 151.7899327688
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 26.68547275942° = 26°41'5″ = 0.46657363565 rad
Angle ∠ B = β = 76.65876362029° = 76°39'28″ = 1.33879281485 rad
Angle ∠ C = γ = 76.65876362029° = 76°39'28″ = 1.33879281485 rad

Height: ha = 25.29882212813
Height: hb = 11.67661021299
Height: hc = 11.67661021299

Median: ma = 25.29882212813
Median: mb = 15.52441746963
Median: mc = 15.52441746963

Inradius: r = 4.74334164903
Circumradius: R = 13.36106231142

Vertex coordinates: A[26; 0] B[0; 0] C[2.76992307692; 11.67661021299]
Centroid: CG[9.59897435897; 3.89220340433]
Coordinates of the circumscribed circle: U[13; 3.08332207187]
Coordinates of the inscribed circle: I[6; 4.74334164903]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.3155272406° = 153°18'55″ = 0.46657363565 rad
∠ B' = β' = 103.3422363797° = 103°20'32″ = 1.33879281485 rad
∠ C' = γ' = 103.3422363797° = 103°20'32″ = 1.33879281485 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 = 26 ; ; c = 26 ; ;

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

p = a+b+c = 12+26+26 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-12)(32-26)(32-26) } ; ; T = sqrt{ 23040 } = 151.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 151.79 }{ 12 } = 25.3 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 151.79 }{ 26 } = 11.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 151.79 }{ 26 } = 11.68 ; ;

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**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 26° 41'5" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-12**2-26**2 }{ 2 * 12 * 26 } ) = 76° 39'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-12**2-26**2 }{ 2 * 26 * 12 } ) = 76° 39'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 151.79 }{ 32 } = 4.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 26° 41'5" } = 13.36 ; ;




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