14 29 30 triangle

Acute scalene triangle.

Sides: a = 14   b = 29   c = 30

Area: T = 200.0989823579
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 27.38655979365° = 27°23'8″ = 0.47879688516 rad
Angle ∠ B = β = 72.32877617415° = 72°19'40″ = 1.2622357583 rad
Angle ∠ C = γ = 80.2876640322° = 80°17'12″ = 1.4011266219 rad

Height: ha = 28.58442605113
Height: hb = 13.79992981779
Height: hc = 13.3399321572

Median: ma = 28.66218212959
Median: mb = 18.37879759495
Median: mc = 17.1321841699

Inradius: r = 5.48219129748
Circumradius: R = 15.21881652496

Vertex coordinates: A[30; 0] B[0; 0] C[4.25; 13.3399321572]
Centroid: CG[11.41766666667; 4.4466440524]
Coordinates of the circumscribed circle: U[15; 2.56875968463]
Coordinates of the inscribed circle: I[7.5; 5.48219129748]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.6144402064° = 152°36'52″ = 0.47879688516 rad
∠ B' = β' = 107.6722238259° = 107°40'20″ = 1.2622357583 rad
∠ C' = γ' = 99.7133359678° = 99°42'48″ = 1.4011266219 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 = 29 ; ; c = 30 ; ;

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

p = a+b+c = 14+29+30 = 73 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 73 }{ 2 } = 36.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36.5 * (36.5-14)(36.5-29)(36.5-30) } ; ; T = sqrt{ 40035.94 } = 200.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 200.09 }{ 14 } = 28.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 200.09 }{ 29 } = 13.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 200.09 }{ 30 } = 13.34 ; ;

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**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 27° 23'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-14**2-30**2 }{ 2 * 14 * 30 } ) = 72° 19'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-14**2-29**2 }{ 2 * 29 * 14 } ) = 80° 17'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 200.09 }{ 36.5 } = 5.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 27° 23'8" } = 15.22 ; ;




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