14 14 26 triangle

Obtuse isosceles triangle.

Sides: a = 14   b = 14   c = 26

Area: T = 67.55499814952
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 21.78767892983° = 21°47'12″ = 0.38802512067 rad
Angle ∠ B = β = 21.78767892983° = 21°47'12″ = 0.38802512067 rad
Angle ∠ C = γ = 136.4266421403° = 136°25'35″ = 2.38110902402 rad

Height: ha = 9.65499973565
Height: hb = 9.65499973565
Height: hc = 5.19661524227

Median: ma = 19.67223155729
Median: mb = 19.67223155729
Median: mc = 5.19661524227

Inradius: r = 2.50218511665
Circumradius: R = 18.86601087935

Vertex coordinates: A[26; 0] B[0; 0] C[13; 5.19661524227]
Centroid: CG[13; 1.73220508076]
Coordinates of the circumscribed circle: U[13; -13.66439563708]
Coordinates of the inscribed circle: I[13; 2.50218511665]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.2133210702° = 158°12'48″ = 0.38802512067 rad
∠ B' = β' = 158.2133210702° = 158°12'48″ = 0.38802512067 rad
∠ C' = γ' = 43.57435785965° = 43°34'25″ = 2.38110902402 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 = 14 ; ; b = 14 ; ; c = 26 ; ;

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

p = a+b+c = 14+14+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 * (27-14)(27-14)(27-26) } ; ; T = sqrt{ 4563 } = 67.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 67.55 }{ 14 } = 9.65 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 67.55 }{ 14 } = 9.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 67.55 }{ 26 } = 5.2 ; ;

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{ 14**2-14**2-26**2 }{ 2 * 14 * 26 } ) = 21° 47'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-14**2-26**2 }{ 2 * 14 * 26 } ) = 21° 47'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-14**2-14**2 }{ 2 * 14 * 14 } ) = 136° 25'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 67.55 }{ 27 } = 2.5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 21° 47'12" } = 18.86 ; ;




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