26 26 27 triangle

Acute isosceles triangle.

Sides: a = 26   b = 26   c = 27

Area: T = 299.9776561584
Perimeter: p = 79
Semiperimeter: s = 39.5

Angle ∠ A = α = 58.7199332848° = 58°43'10″ = 1.02548456928 rad
Angle ∠ B = β = 58.7199332848° = 58°43'10″ = 1.02548456928 rad
Angle ∠ C = γ = 62.56113343041° = 62°33'41″ = 1.0921901268 rad

Height: ha = 23.07551201219
Height: hb = 23.07551201219
Height: hc = 22.22204860433

Median: ma = 23.09876189249
Median: mb = 23.09876189249
Median: mc = 22.22204860433

Inradius: r = 7.59443433313
Circumradius: R = 15.21111884205

Vertex coordinates: A[27; 0] B[0; 0] C[13.5; 22.22204860433]
Centroid: CG[13.5; 7.40768286811]
Coordinates of the circumscribed circle: U[13.5; 7.00992976228]
Coordinates of the inscribed circle: I[13.5; 7.59443433313]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.2810667152° = 121°16'50″ = 1.02548456928 rad
∠ B' = β' = 121.2810667152° = 121°16'50″ = 1.02548456928 rad
∠ C' = γ' = 117.4398665696° = 117°26'19″ = 1.0921901268 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 = 26 ; ; b = 26 ; ; c = 27 ; ;

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

p = a+b+c = 26+26+27 = 79 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 79 }{ 2 } = 39.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39.5 * (39.5-26)(39.5-26)(39.5-27) } ; ; T = sqrt{ 89985.94 } = 299.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 299.98 }{ 26 } = 23.08 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 299.98 }{ 26 } = 23.08 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 299.98 }{ 27 } = 22.22 ; ;

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{ 26**2-26**2-27**2 }{ 2 * 26 * 27 } ) = 58° 43'10" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-26**2-27**2 }{ 2 * 26 * 27 } ) = 58° 43'10" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 62° 33'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 299.98 }{ 39.5 } = 7.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 26 }{ 2 * sin 58° 43'10" } = 15.21 ; ;




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