16 21 29 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 21   c = 29

Area: T = 164.0987531974
Perimeter: p = 66
Semiperimeter: s = 33

Angle ∠ A = α = 32.60993428437° = 32°36'34″ = 0.56991403995 rad
Angle ∠ B = β = 45.01770320401° = 45°1'1″ = 0.78656954286 rad
Angle ∠ C = γ = 102.3743625116° = 102°22'25″ = 1.78767568255 rad

Height: ha = 20.51221914968
Height: hb = 15.62883363785
Height: hc = 11.31770711706

Median: ma = 24.02108242989
Median: mb = 20.93444214155
Median: mc = 11.75879760163

Inradius: r = 4.97326524841
Circumradius: R = 14.84548302098

Vertex coordinates: A[29; 0] B[0; 0] C[11.31103448276; 11.31770711706]
Centroid: CG[13.43767816092; 3.77223570569]
Coordinates of the circumscribed circle: U[14.5; -3.1811035045]
Coordinates of the inscribed circle: I[12; 4.97326524841]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.3910657156° = 147°23'26″ = 0.56991403995 rad
∠ B' = β' = 134.983296796° = 134°58'59″ = 0.78656954286 rad
∠ C' = γ' = 77.62663748838° = 77°37'35″ = 1.78767568255 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 = 16 ; ; b = 21 ; ; c = 29 ; ;

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

p = a+b+c = 16+21+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 * (33-16)(33-21)(33-29) } ; ; T = sqrt{ 26928 } = 164.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 164.1 }{ 16 } = 20.51 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 164.1 }{ 21 } = 15.63 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 164.1 }{ 29 } = 11.32 ; ;

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{ 16**2-21**2-29**2 }{ 2 * 21 * 29 } ) = 32° 36'34" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-16**2-29**2 }{ 2 * 16 * 29 } ) = 45° 1'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-16**2-21**2 }{ 2 * 21 * 16 } ) = 102° 22'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 164.1 }{ 33 } = 4.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 32° 36'34" } = 14.84 ; ;




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