14 27 29 triangle

Acute scalene triangle.

Sides: a = 14   b = 27   c = 29

Area: T = 187.832971011
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 28.67703405832° = 28°40'13″ = 0.55003918408 rad
Angle ∠ B = β = 67.70990296252° = 67°42'33″ = 1.18217455003 rad
Angle ∠ C = γ = 83.62106297916° = 83°37'14″ = 1.45994553125 rad

Height: ha = 26.833281573
Height: hb = 13.913331186
Height: hc = 12.9543773111

Median: ma = 27.12993199325
Median: mb = 18.33771208209
Median: mc = 15.88223801743

Inradius: r = 5.3676563146
Circumradius: R = 14.59903435532

Vertex coordinates: A[29; 0] B[0; 0] C[5.31103448276; 12.9543773111]
Centroid: CG[11.43767816092; 4.31879243703]
Coordinates of the circumscribed circle: U[14.5; 1.62111492837]
Coordinates of the inscribed circle: I[8; 5.3676563146]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.3329659417° = 151°19'47″ = 0.55003918408 rad
∠ B' = β' = 112.2910970375° = 112°17'27″ = 1.18217455003 rad
∠ C' = γ' = 96.37993702084° = 96°22'46″ = 1.45994553125 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 = 27 ; ; c = 29 ; ;

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

p = a+b+c = 14+27+29 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-14)(35-27)(35-29) } ; ; T = sqrt{ 35280 } = 187.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 187.83 }{ 14 } = 26.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 187.83 }{ 27 } = 13.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 187.83 }{ 29 } = 12.95 ; ;

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**2-27**2-29**2 }{ 2 * 27 * 29 } ) = 28° 40'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-14**2-29**2 }{ 2 * 14 * 29 } ) = 67° 42'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-14**2-27**2 }{ 2 * 27 * 14 } ) = 83° 37'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 187.83 }{ 35 } = 5.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 28° 40'13" } = 14.59 ; ;




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