17 23 23 triangle

Acute isosceles triangle.

Sides: a = 17   b = 23   c = 23

Area: T = 181.6659537322
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 43.37876112363° = 43°22'39″ = 0.75770821377 rad
Angle ∠ B = β = 68.31111943819° = 68°18'40″ = 1.19222552579 rad
Angle ∠ C = γ = 68.31111943819° = 68°18'40″ = 1.19222552579 rad

Height: ha = 21.37217102732
Height: hb = 15.79664815063
Height: hc = 15.79664815063

Median: ma = 21.37217102732
Median: mb = 16.63658047596
Median: mc = 16.63658047596

Inradius: r = 5.76769694388
Circumradius: R = 12.37661737652

Vertex coordinates: A[23; 0] B[0; 0] C[6.28326086957; 15.79664815063]
Centroid: CG[9.76108695652; 5.26554938354]
Coordinates of the circumscribed circle: U[11.5; 4.5743803348]
Coordinates of the inscribed circle: I[8.5; 5.76769694388]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.6222388764° = 136°37'21″ = 0.75770821377 rad
∠ B' = β' = 111.6898805618° = 111°41'20″ = 1.19222552579 rad
∠ C' = γ' = 111.6898805618° = 111°41'20″ = 1.19222552579 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 = 17 ; ; b = 23 ; ; c = 23 ; ;

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

p = a+b+c = 17+23+23 = 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 * (31.5-17)(31.5-23)(31.5-23) } ; ; T = sqrt{ 33000.19 } = 181.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 181.66 }{ 17 } = 21.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 181.66 }{ 23 } = 15.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 181.66 }{ 23 } = 15.8 ; ;

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{ 17**2-23**2-23**2 }{ 2 * 23 * 23 } ) = 43° 22'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-17**2-23**2 }{ 2 * 17 * 23 } ) = 68° 18'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-17**2-23**2 }{ 2 * 23 * 17 } ) = 68° 18'40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 181.66 }{ 31.5 } = 5.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 43° 22'39" } = 12.38 ; ;




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