17 29 29 triangle

Acute isosceles triangle.

Sides: a = 17   b = 29   c = 29

Area: T = 235.6743900761
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 34.08876932302° = 34°5'16″ = 0.59549424813 rad
Angle ∠ B = β = 72.95661533849° = 72°57'22″ = 1.27333250862 rad
Angle ∠ C = γ = 72.95661533849° = 72°57'22″ = 1.27333250862 rad

Height: ha = 27.7266341266
Height: hb = 16.25333724663
Height: hc = 16.25333724663

Median: ma = 27.7266341266
Median: mb = 18.83548082018
Median: mc = 18.83548082018

Inradius: r = 6.28546373536
Circumradius: R = 15.16660832551

Vertex coordinates: A[29; 0] B[0; 0] C[4.98327586207; 16.25333724663]
Centroid: CG[11.32875862069; 5.41877908221]
Coordinates of the circumscribed circle: U[14.5; 4.44552312989]
Coordinates of the inscribed circle: I[8.5; 6.28546373536]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.912230677° = 145°54'44″ = 0.59549424813 rad
∠ B' = β' = 107.0443846615° = 107°2'38″ = 1.27333250862 rad
∠ C' = γ' = 107.0443846615° = 107°2'38″ = 1.27333250862 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 = 29 ; ; c = 29 ; ;

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

p = a+b+c = 17+29+29 = 75 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 75 }{ 2 } = 37.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.5 * (37.5-17)(37.5-29)(37.5-29) } ; ; T = sqrt{ 55542.19 } = 235.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 235.67 }{ 17 } = 27.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 235.67 }{ 29 } = 16.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 235.67 }{ 29 } = 16.25 ; ;

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**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 34° 5'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-17**2-29**2 }{ 2 * 17 * 29 } ) = 72° 57'22" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-17**2-29**2 }{ 2 * 29 * 17 } ) = 72° 57'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 235.67 }{ 37.5 } = 6.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 34° 5'16" } = 15.17 ; ;




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