6 28 29 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 28   c = 29

Area: T = 83.8365776969
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 11.91768568685° = 11°55'1″ = 0.20879883888 rad
Angle ∠ B = β = 74.5499821433° = 74°29'59″ = 1.33002671762 rad
Angle ∠ C = γ = 93.58333216985° = 93°35' = 1.63333370886 rad

Height: ha = 27.94552589897
Height: hb = 5.98882697835
Height: hc = 5.7821777722

Median: ma = 28.34660755661
Median: mb = 15.57224115024
Median: mc = 14.13332940251

Inradius: r = 2.66114532371
Circumradius: R = 14.52884035532

Vertex coordinates: A[29; 0] B[0; 0] C[1.60334482759; 5.7821777722]
Centroid: CG[10.20111494253; 1.92772592407]
Coordinates of the circumscribed circle: U[14.5; -0.90880252221]
Coordinates of the inscribed circle: I[3.5; 2.66114532371]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.0833143131° = 168°4'59″ = 0.20879883888 rad
∠ B' = β' = 105.5500178567° = 105°30'1″ = 1.33002671762 rad
∠ C' = γ' = 86.41766783015° = 86°25' = 1.63333370886 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 = 6 ; ; b = 28 ; ; c = 29 ; ;

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

p = a+b+c = 6+28+29 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-6)(31.5-28)(31.5-29) } ; ; T = sqrt{ 7028.44 } = 83.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 83.84 }{ 6 } = 27.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 83.84 }{ 28 } = 5.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 83.84 }{ 29 } = 5.78 ; ;

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{ 6**2-28**2-29**2 }{ 2 * 28 * 29 } ) = 11° 55'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-6**2-29**2 }{ 2 * 6 * 29 } ) = 74° 29'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-6**2-28**2 }{ 2 * 28 * 6 } ) = 93° 35' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 83.84 }{ 31.5 } = 2.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 11° 55'1" } = 14.53 ; ;




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