26 26 28 triangle

Acute isosceles triangle.

Sides: a = 26   b = 26   c = 28

Area: T = 306.7254632203
Perimeter: p = 80
Semiperimeter: s = 40

Angle ∠ A = α = 57.42110296072° = 57°25'16″ = 1.00221860265 rad
Angle ∠ B = β = 57.42110296072° = 57°25'16″ = 1.00221860265 rad
Angle ∠ C = γ = 65.15879407856° = 65°9'29″ = 1.13772206005 rad

Height: ha = 23.59442024771
Height: hb = 23.59442024771
Height: hc = 21.90989023002

Median: ma = 23.68554385647
Median: mb = 23.68554385647
Median: mc = 21.90989023002

Inradius: r = 7.66881158051
Circumradius: R = 15.42875187031

Vertex coordinates: A[28; 0] B[0; 0] C[14; 21.90989023002]
Centroid: CG[14; 7.30329674334]
Coordinates of the circumscribed circle: U[14; 6.48113835971]
Coordinates of the inscribed circle: I[14; 7.66881158051]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.5798970393° = 122°34'44″ = 1.00221860265 rad
∠ B' = β' = 122.5798970393° = 122°34'44″ = 1.00221860265 rad
∠ C' = γ' = 114.8422059214° = 114°50'31″ = 1.13772206005 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 = 28 ; ;

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

p = a+b+c = 26+26+28 = 80 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 80 }{ 2 } = 40 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 40 * (40-26)(40-26)(40-28) } ; ; T = sqrt{ 94080 } = 306.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 306.72 }{ 26 } = 23.59 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 306.72 }{ 26 } = 23.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 306.72 }{ 28 } = 21.91 ; ;

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**2-28**2 }{ 2 * 26 * 28 } ) = 57° 25'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-26**2-28**2 }{ 2 * 26 * 28 } ) = 57° 25'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 65° 9'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 306.72 }{ 40 } = 7.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 26 }{ 2 * sin 57° 25'16" } = 15.43 ; ;




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