6 29 29 triangle

Acute isosceles triangle.

Sides: a = 6   b = 29   c = 29

Area: T = 86.53332306111
Perimeter: p = 64
Semiperimeter: s = 32

Angle ∠ A = α = 11.87655449032° = 11°52'32″ = 0.2077267359 rad
Angle ∠ B = β = 84.06222275484° = 84°3'44″ = 1.46771626473 rad
Angle ∠ C = γ = 84.06222275484° = 84°3'44″ = 1.46771626473 rad

Height: ha = 28.84444102037
Height: hb = 5.96878090077
Height: hc = 5.96878090077

Median: ma = 28.84444102037
Median: mb = 15.10879449297
Median: mc = 15.10879449297

Inradius: r = 2.70441634566
Circumradius: R = 14.5788214532

Vertex coordinates: A[29; 0] B[0; 0] C[0.62106896552; 5.96878090077]
Centroid: CG[9.87435632184; 1.98992696692]
Coordinates of the circumscribed circle: U[14.5; 1.50880911585]
Coordinates of the inscribed circle: I[3; 2.70441634566]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.1244455097° = 168°7'28″ = 0.2077267359 rad
∠ B' = β' = 95.93877724516° = 95°56'16″ = 1.46771626473 rad
∠ C' = γ' = 95.93877724516° = 95°56'16″ = 1.46771626473 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 = 29 ; ;

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

p = a+b+c = 6+29+29 = 64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 64 }{ 2 } = 32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32 * (32-6)(32-29)(32-29) } ; ; T = sqrt{ 7488 } = 86.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 86.53 }{ 6 } = 28.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 86.53 }{ 29 } = 5.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 86.53 }{ 29 } = 5.97 ; ;

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**2-29**2 }{ 2 * 29 * 29 } ) = 11° 52'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-6**2-29**2 }{ 2 * 6 * 29 } ) = 84° 3'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-6**2-29**2 }{ 2 * 29 * 6 } ) = 84° 3'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 86.53 }{ 32 } = 2.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6 }{ 2 * sin 11° 52'32" } = 14.58 ; ;




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