23 29 29 triangle

Acute isosceles triangle.

Sides: a = 23   b = 29   c = 29

Area: T = 306.1577128775
Perimeter: p = 81
Semiperimeter: s = 40.5

Angle ∠ A = α = 46.726557264° = 46°43'32″ = 0.81655150874 rad
Angle ∠ B = β = 66.637721368° = 66°38'14″ = 1.16330387831 rad
Angle ∠ C = γ = 66.637721368° = 66°38'14″ = 1.16330387831 rad

Height: ha = 26.62223590239
Height: hb = 21.11442847431
Height: hc = 21.11442847431

Median: ma = 26.62223590239
Median: mb = 21.78987585695
Median: mc = 21.78987585695

Inradius: r = 7.55994352784
Circumradius: R = 15.79549939606

Vertex coordinates: A[29; 0] B[0; 0] C[9.12106896552; 21.11442847431]
Centroid: CG[12.70768965517; 7.03880949144]
Coordinates of the circumscribed circle: U[14.5; 6.26435320878]
Coordinates of the inscribed circle: I[11.5; 7.55994352784]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 133.274442736° = 133°16'28″ = 0.81655150874 rad
∠ B' = β' = 113.363278632° = 113°21'46″ = 1.16330387831 rad
∠ C' = γ' = 113.363278632° = 113°21'46″ = 1.16330387831 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 = 23 ; ; b = 29 ; ; c = 29 ; ;

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

p = a+b+c = 23+29+29 = 81 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 81 }{ 2 } = 40.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 40.5 * (40.5-23)(40.5-29)(40.5-29) } ; ; T = sqrt{ 93732.19 } = 306.16 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 306.16 }{ 23 } = 26.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 306.16 }{ 29 } = 21.11 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 306.16 }{ 29 } = 21.11 ; ;

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{ 23**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 46° 43'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-23**2-29**2 }{ 2 * 23 * 29 } ) = 66° 38'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-23**2-29**2 }{ 2 * 29 * 23 } ) = 66° 38'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 306.16 }{ 40.5 } = 7.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 23 }{ 2 * sin 46° 43'32" } = 15.79 ; ;




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