14 28 29 triangle

Acute scalene triangle.

Sides: a = 14   b = 28   c = 29

Area: T = 192.8954887179
Perimeter: p = 71
Semiperimeter: s = 35.5

Angle ∠ A = α = 28.36765487929° = 28°22' = 0.49550896739 rad
Angle ∠ B = β = 71.84657453531° = 71°50'45″ = 1.254394481 rad
Angle ∠ C = γ = 79.7887705854° = 79°47'16″ = 1.39325581698 rad

Height: ha = 27.55664124542
Height: hb = 13.77882062271
Height: hc = 13.30330956676

Median: ma = 27.63215037593
Median: mb = 17.95882849961
Median: mc = 16.72657286837

Inradius: r = 5.43436587938
Circumradius: R = 14.73334128009

Vertex coordinates: A[29; 0] B[0; 0] C[4.36220689655; 13.30330956676]
Centroid: CG[11.12106896552; 4.43443652225]
Coordinates of the circumscribed circle: U[14.5; 2.61221739532]
Coordinates of the inscribed circle: I[7.5; 5.43436587938]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.6333451207° = 151°38' = 0.49550896739 rad
∠ B' = β' = 108.1544254647° = 108°9'15″ = 1.254394481 rad
∠ C' = γ' = 100.2122294146° = 100°12'44″ = 1.39325581698 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 = 28 ; ; c = 29 ; ;

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

p = a+b+c = 14+28+29 = 71 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 71 }{ 2 } = 35.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35.5 * (35.5-14)(35.5-28)(35.5-29) } ; ; T = sqrt{ 37208.44 } = 192.89 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 192.89 }{ 14 } = 27.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 192.89 }{ 28 } = 13.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 192.89 }{ 29 } = 13.3 ; ;

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**2-28**2-29**2 }{ 2 * 28 * 29 } ) = 28° 22' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-14**2-29**2 }{ 2 * 14 * 29 } ) = 71° 50'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-14**2-28**2 }{ 2 * 28 * 14 } ) = 79° 47'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 192.89 }{ 35.5 } = 5.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 28° 22' } = 14.73 ; ;




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