14 26 26 triangle

Acute isosceles triangle.

Sides: a = 14   b = 26   c = 26

Area: T = 175.2879776358
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 31.23769965513° = 31°14'13″ = 0.54551884383 rad
Angle ∠ B = β = 74.38215017244° = 74°22'53″ = 1.29882021077 rad
Angle ∠ C = γ = 74.38215017244° = 74°22'53″ = 1.29882021077 rad

Height: ha = 25.04399680511
Height: hb = 13.48330597198
Height: hc = 13.48330597198

Median: ma = 25.04399680511
Median: mb = 16.34401346384
Median: mc = 16.34401346384

Inradius: r = 5.31215083745
Circumradius: R = 13.49884197787

Vertex coordinates: A[26; 0] B[0; 0] C[3.76992307692; 13.48330597198]
Centroid: CG[9.92330769231; 4.49443532399]
Coordinates of the circumscribed circle: U[13; 3.63441899404]
Coordinates of the inscribed circle: I[7; 5.31215083745]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.7633003449° = 148°45'47″ = 0.54551884383 rad
∠ B' = β' = 105.6188498276° = 105°37'7″ = 1.29882021077 rad
∠ C' = γ' = 105.6188498276° = 105°37'7″ = 1.29882021077 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 = 26 ; ; c = 26 ; ;

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

p = a+b+c = 14+26+26 = 66 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 66 }{ 2 } = 33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33 * (33-14)(33-26)(33-26) } ; ; T = sqrt{ 30723 } = 175.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 175.28 }{ 14 } = 25.04 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 175.28 }{ 26 } = 13.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 175.28 }{ 26 } = 13.48 ; ;

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**2-26**2-26**2 }{ 2 * 26 * 26 } ) = 31° 14'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-14**2-26**2 }{ 2 * 14 * 26 } ) = 74° 22'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-14**2-26**2 }{ 2 * 26 * 14 } ) = 74° 22'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 175.28 }{ 33 } = 5.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 31° 14'13" } = 13.5 ; ;




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