24 26 26 triangle

Acute isosceles triangle.

Sides: a = 24   b = 26   c = 26

Area: T = 276.7821502272
Perimeter: p = 76
Semiperimeter: s = 38

Angle ∠ A = α = 54.97328525008° = 54°58'22″ = 0.95994572754 rad
Angle ∠ B = β = 62.51435737496° = 62°30'49″ = 1.09110676891 rad
Angle ∠ C = γ = 62.51435737496° = 62°30'49″ = 1.09110676891 rad

Height: ha = 23.06551251893
Height: hb = 21.29108847902
Height: hc = 21.29108847902

Median: ma = 23.06551251893
Median: mb = 21.37875583264
Median: mc = 21.37875583264

Inradius: r = 7.2843723744
Circumradius: R = 14.6544158485

Vertex coordinates: A[26; 0] B[0; 0] C[11.07769230769; 21.29108847902]
Centroid: CG[12.3598974359; 7.09769615967]
Coordinates of the circumscribed circle: U[13; 6.76334577623]
Coordinates of the inscribed circle: I[12; 7.2843723744]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.0277147499° = 125°1'38″ = 0.95994572754 rad
∠ B' = β' = 117.486642625° = 117°29'11″ = 1.09110676891 rad
∠ C' = γ' = 117.486642625° = 117°29'11″ = 1.09110676891 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 = 24 ; ; b = 26 ; ; c = 26 ; ;

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

p = a+b+c = 24+26+26 = 76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 76 }{ 2 } = 38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38 * (38-24)(38-26)(38-26) } ; ; T = sqrt{ 76608 } = 276.78 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 276.78 }{ 24 } = 23.07 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 276.78 }{ 26 } = 21.29 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 276.78 }{ 26 } = 21.29 ; ;

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{ 24**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 54° 58'22" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-24**2-26**2 }{ 2 * 24 * 26 } ) = 62° 30'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-24**2-26**2 }{ 2 * 26 * 24 } ) = 62° 30'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 276.78 }{ 38 } = 7.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24 }{ 2 * sin 54° 58'22" } = 14.65 ; ;




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