14 23 29 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 23   c = 29

Area: T = 158.3676663159
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 28.35504015844° = 28°21'1″ = 0.49548078519 rad
Angle ∠ B = β = 51.27326028553° = 51°16'21″ = 0.89548757359 rad
Angle ∠ C = γ = 100.377699556° = 100°22'37″ = 1.75219090658 rad

Height: ha = 22.62438090227
Height: hb = 13.77110141877
Height: hc = 10.92218388385

Median: ma = 25.21990404258
Median: mb = 19.6533244007
Median: mc = 12.33989626793

Inradius: r = 4.79989897927
Circumradius: R = 14.74111074619

Vertex coordinates: A[29; 0] B[0; 0] C[8.75986206897; 10.92218388385]
Centroid: CG[12.58662068966; 3.64106129462]
Coordinates of the circumscribed circle: U[14.5; -2.65552305366]
Coordinates of the inscribed circle: I[10; 4.79989897927]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.6549598416° = 151°38'59″ = 0.49548078519 rad
∠ B' = β' = 128.7277397145° = 128°43'39″ = 0.89548757359 rad
∠ C' = γ' = 79.62330044397° = 79°37'23″ = 1.75219090658 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 = 23 ; ; c = 29 ; ;

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

p = a+b+c = 14+23+29 = 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)(33-23)(33-29) } ; ; T = sqrt{ 25080 } = 158.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 158.37 }{ 14 } = 22.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 158.37 }{ 23 } = 13.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 158.37 }{ 29 } = 10.92 ; ;

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**2-23**2-29**2 }{ 2 * 23 * 29 } ) = 28° 21'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-14**2-29**2 }{ 2 * 14 * 29 } ) = 51° 16'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-14**2-23**2 }{ 2 * 23 * 14 } ) = 100° 22'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 158.37 }{ 33 } = 4.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 28° 21'1" } = 14.74 ; ;




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