2 26 26 triangle

Acute isosceles triangle.

Sides: a = 2   b = 26   c = 26

Area: T = 25.98107621135
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 4.40884550079° = 4°24'30″ = 0.07769420548 rad
Angle ∠ B = β = 87.7965772496° = 87°47'45″ = 1.53223252994 rad
Angle ∠ C = γ = 87.7965772496° = 87°47'45″ = 1.53223252994 rad

Height: ha = 25.98107621135
Height: hb = 1.99985201626
Height: hc = 1.99985201626

Median: ma = 25.98107621135
Median: mb = 13.07766968306
Median: mc = 13.07766968306

Inradius: r = 0.96222504486
Circumradius: R = 13.01096260657

Vertex coordinates: A[26; 0] B[0; 0] C[0.07769230769; 1.99985201626]
Centroid: CG[8.69223076923; 0.66661733875]
Coordinates of the circumscribed circle: U[13; 0.55003702333]
Coordinates of the inscribed circle: I[1; 0.96222504486]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.5921544992° = 175°35'30″ = 0.07769420548 rad
∠ B' = β' = 92.2044227504° = 92°12'15″ = 1.53223252994 rad
∠ C' = γ' = 92.2044227504° = 92°12'15″ = 1.53223252994 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 = 2 ; ; b = 26 ; ; c = 26 ; ;

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

p = a+b+c = 2+26+26 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-2)(27-26)(27-26) } ; ; T = sqrt{ 675 } = 25.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25.98 }{ 2 } = 25.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25.98 }{ 26 } = 2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25.98 }{ 26 } = 2 ; ;

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{ 2**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 4° 24'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-2**2-26**2 }{ 2 * 2 * 26 } ) = 87° 47'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-2**2-26**2 }{ 2 * 26 * 2 } ) = 87° 47'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25.98 }{ 27 } = 0.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 4° 24'30" } = 13.01 ; ;




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