14 21 29 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 21   c = 29

Area: T = 137.8769503517
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 26.92217628128° = 26°55'18″ = 0.47698734015 rad
Angle ∠ B = β = 42.77880463452° = 42°46'41″ = 0.74766177563 rad
Angle ∠ C = γ = 110.3300190842° = 110°18'1″ = 1.92551014958 rad

Height: ha = 19.69656433596
Height: hb = 13.13304289064
Height: hc = 9.50882416219

Median: ma = 24.33110501212
Median: mb = 20.20551973512
Median: mc = 10.40443260233

Inradius: r = 4.30884219849
Circumradius: R = 15.46602718196

Vertex coordinates: A[29; 0] B[0; 0] C[10.2765862069; 9.50882416219]
Centroid: CG[13.0921954023; 3.1699413874]
Coordinates of the circumscribed circle: U[14.5; -5.36437677741]
Coordinates of the inscribed circle: I[11; 4.30884219849]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.0788237187° = 153°4'42″ = 0.47698734015 rad
∠ B' = β' = 137.2221953655° = 137°13'19″ = 0.74766177563 rad
∠ C' = γ' = 69.76998091581° = 69°41'59″ = 1.92551014958 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 = 21 ; ; c = 29 ; ;

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

p = a+b+c = 14+21+29 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-14)(32-21)(32-29) } ; ; T = sqrt{ 19008 } = 137.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 137.87 }{ 14 } = 19.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 137.87 }{ 21 } = 13.13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 137.87 }{ 29 } = 9.51 ; ;

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**2-21**2-29**2 }{ 2 * 21 * 29 } ) = 26° 55'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-14**2-29**2 }{ 2 * 14 * 29 } ) = 42° 46'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-14**2-21**2 }{ 2 * 21 * 14 } ) = 110° 18'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 137.87 }{ 32 } = 4.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 26° 55'18" } = 15.46 ; ;




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