26 27 27 triangle

Acute isosceles triangle.

Sides: a = 26   b = 27   c = 27

Area: T = 307.6366148721
Perimeter: p = 80
Semiperimeter: s = 40

Angle ∠ A = α = 57.56444093612° = 57°33'52″ = 1.00546884753 rad
Angle ∠ B = β = 61.21877953194° = 61°13'4″ = 1.06884520891 rad
Angle ∠ C = γ = 61.21877953194° = 61°13'4″ = 1.06884520891 rad

Height: ha = 23.66443191324
Height: hb = 22.78878628682
Height: hc = 22.78878628682

Median: ma = 23.66443191324
Median: mb = 22.80989894559
Median: mc = 22.80989894559

Inradius: r = 7.6910903718
Circumradius: R = 15.40329362924

Vertex coordinates: A[27; 0] B[0; 0] C[12.51985185185; 22.78878628682]
Centroid: CG[13.17328395062; 7.59659542894]
Coordinates of the circumscribed circle: U[13.5; 7.41662285852]
Coordinates of the inscribed circle: I[13; 7.6910903718]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 122.4365590639° = 122°26'8″ = 1.00546884753 rad
∠ B' = β' = 118.7822204681° = 118°46'56″ = 1.06884520891 rad
∠ C' = γ' = 118.7822204681° = 118°46'56″ = 1.06884520891 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 = 27 ; ; c = 27 ; ;

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

p = a+b+c = 26+27+27 = 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)(40-27)(40-27) } ; ; T = sqrt{ 94640 } = 307.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 307.64 }{ 26 } = 23.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 307.64 }{ 27 } = 22.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 307.64 }{ 27 } = 22.79 ; ;

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**2-27**2-27**2 }{ 2 * 27 * 27 } ) = 57° 33'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-26**2-27**2 }{ 2 * 26 * 27 } ) = 61° 13'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-26**2-27**2 }{ 2 * 27 * 26 } ) = 61° 13'4" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 307.64 }{ 40 } = 7.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 26 }{ 2 * sin 57° 33'52" } = 15.4 ; ;




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