16 22 29 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 22   c = 29

Area: T = 174.1799325696
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 33.09441684217° = 33°5'39″ = 0.57876022022 rad
Angle ∠ B = β = 48.65773781163° = 48°39'27″ = 0.84992314535 rad
Angle ∠ C = γ = 98.2488453462° = 98°14'54″ = 1.71547589979 rad

Height: ha = 21.7722415712
Height: hb = 15.83444841542
Height: hc = 12.01223672894

Median: ma = 24.46442596455
Median: mb = 20.67660731281
Median: mc = 12.63992246598

Inradius: r = 5.19993828566
Circumradius: R = 14.65215666529

Vertex coordinates: A[29; 0] B[0; 0] C[10.56989655172; 12.01223672894]
Centroid: CG[13.19896551724; 4.00441224298]
Coordinates of the circumscribed circle: U[14.5; -2.10220003295]
Coordinates of the inscribed circle: I[11.5; 5.19993828566]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.9065831578° = 146°54'21″ = 0.57876022022 rad
∠ B' = β' = 131.3432621884° = 131°20'33″ = 0.84992314535 rad
∠ C' = γ' = 81.7521546538° = 81°45'6″ = 1.71547589979 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 = 22 ; ; c = 29 ; ;

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

p = a+b+c = 16+22+29 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-16)(33.5-22)(33.5-29) } ; ; T = sqrt{ 30338.44 } = 174.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 174.18 }{ 16 } = 21.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 174.18 }{ 22 } = 15.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 174.18 }{ 29 } = 12.01 ; ;

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**2-22**2-29**2 }{ 2 * 22 * 29 } ) = 33° 5'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-16**2-29**2 }{ 2 * 16 * 29 } ) = 48° 39'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-16**2-22**2 }{ 2 * 22 * 16 } ) = 98° 14'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 174.18 }{ 33.5 } = 5.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 33° 5'39" } = 14.65 ; ;




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