9 29 29 triangle

Acute isosceles triangle.

Sides: a = 9   b = 29   c = 29

Area: T = 128.9199306157
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 17.85435916421° = 17°51'13″ = 0.31216039575 rad
Angle ∠ B = β = 81.0733204179° = 81°4'24″ = 1.41549943481 rad
Angle ∠ C = γ = 81.0733204179° = 81°4'24″ = 1.41549943481 rad

Height: ha = 28.64987347016
Height: hb = 8.89109866315
Height: hc = 8.89109866315

Median: ma = 28.64987347016
Median: mb = 15.83550876221
Median: mc = 15.83550876221

Inradius: r = 3.84883374972
Circumradius: R = 14.67877861005

Vertex coordinates: A[29; 0] B[0; 0] C[1.39765517241; 8.89109866315]
Centroid: CG[10.1322183908; 2.96436622105]
Coordinates of the circumscribed circle: U[14.5; 2.27875874984]
Coordinates of the inscribed circle: I[4.5; 3.84883374972]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.1466408358° = 162°8'47″ = 0.31216039575 rad
∠ B' = β' = 98.9276795821° = 98°55'36″ = 1.41549943481 rad
∠ C' = γ' = 98.9276795821° = 98°55'36″ = 1.41549943481 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 = 9 ; ; b = 29 ; ; c = 29 ; ;

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

p = a+b+c = 9+29+29 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-9)(33.5-29)(33.5-29) } ; ; T = sqrt{ 16620.19 } = 128.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 128.92 }{ 9 } = 28.65 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 128.92 }{ 29 } = 8.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 128.92 }{ 29 } = 8.89 ; ;

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{ 9**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 17° 51'13" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-9**2-29**2 }{ 2 * 9 * 29 } ) = 81° 4'24" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-9**2-29**2 }{ 2 * 29 * 9 } ) = 81° 4'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 128.92 }{ 33.5 } = 3.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 17° 51'13" } = 14.68 ; ;




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