6 29 30 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 29   c = 30

Area: T = 86.81097776751
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 11.51113885177° = 11°30'41″ = 0.20109116311 rad
Angle ∠ B = β = 74.69990591483° = 74°41'57″ = 1.30437445303 rad
Angle ∠ C = γ = 93.7989552334° = 93°47'22″ = 1.63769364922 rad

Height: ha = 28.93765925584
Height: hb = 5.9876881219
Height: hc = 5.78773185117

Median: ma = 29.35113202429
Median: mb = 16.0554594358
Median: mc = 14.61216391962

Inradius: r = 2.67110700823
Circumradius: R = 15.0332868819

Vertex coordinates: A[30; 0] B[0; 0] C[1.58333333333; 5.78773185117]
Centroid: CG[10.52877777778; 1.92991061706]
Coordinates of the circumscribed circle: U[15; -0.99435516748]
Coordinates of the inscribed circle: I[3.5; 2.67110700823]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.4898611482° = 168°29'19″ = 0.20109116311 rad
∠ B' = β' = 105.3010940852° = 105°18'3″ = 1.30437445303 rad
∠ C' = γ' = 86.2110447666° = 86°12'38″ = 1.63769364922 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 = 29 ; ; c = 30 ; ;

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

p = a+b+c = 6+29+30 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-6)(32.5-29)(32.5-30) } ; ; T = sqrt{ 7535.94 } = 86.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 86.81 }{ 6 } = 28.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 86.81 }{ 29 } = 5.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 86.81 }{ 30 } = 5.79 ; ;

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**2-29**2-30**2 }{ 2 * 29 * 30 } ) = 11° 30'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-6**2-30**2 }{ 2 * 6 * 30 } ) = 74° 41'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-6**2-29**2 }{ 2 * 29 * 6 } ) = 93° 47'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 86.81 }{ 32.5 } = 2.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 11° 30'41" } = 15.03 ; ;




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