14 26 29 triangle

Acute scalene triangle.

Sides: a = 14   b = 26   c = 29

Area: T = 181.8354918264
Perimeter: p = 69
Semiperimeter: s = 34.5

Angle ∠ A = α = 28.83770830876° = 28°50'13″ = 0.50333020465 rad
Angle ∠ B = β = 63.60334476543° = 63°36'12″ = 1.11100895772 rad
Angle ∠ C = γ = 87.55994692581° = 87°33'34″ = 1.52882010299 rad

Height: ha = 25.97664168948
Height: hb = 13.98773014049
Height: hc = 12.54403391906

Median: ma = 26.63664412037
Median: mb = 18.69549190958
Median: mc = 15.02549792013

Inradius: r = 5.2710577341
Circumradius: R = 14.51331640567

Vertex coordinates: A[29; 0] B[0; 0] C[6.2244137931; 12.54403391906]
Centroid: CG[11.74113793103; 4.18801130635]
Coordinates of the circumscribed circle: U[14.5; 0.61880056123]
Coordinates of the inscribed circle: I[8.5; 5.2710577341]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.1632916912° = 151°9'47″ = 0.50333020465 rad
∠ B' = β' = 116.3976552346° = 116°23'48″ = 1.11100895772 rad
∠ C' = γ' = 92.44105307419° = 92°26'26″ = 1.52882010299 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 = 29 ; ;

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

p = a+b+c = 14+26+29 = 69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 69 }{ 2 } = 34.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.5 * (34.5-14)(34.5-26)(34.5-29) } ; ; T = sqrt{ 33063.94 } = 181.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 181.83 }{ 14 } = 25.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 181.83 }{ 26 } = 13.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 181.83 }{ 29 } = 12.54 ; ;

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**2-29**2 }{ 2 * 26 * 29 } ) = 28° 50'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-14**2-29**2 }{ 2 * 14 * 29 } ) = 63° 36'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-14**2-26**2 }{ 2 * 26 * 14 } ) = 87° 33'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 181.83 }{ 34.5 } = 5.27 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 28° 50'13" } = 14.51 ; ;




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