2 29 29 triangle

Acute isosceles triangle.

Sides: a = 2   b = 29   c = 29

Area: T = 28.98327534924
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 3.95222165714° = 3°57'8″ = 0.06989791919 rad
Angle ∠ B = β = 88.02438917143° = 88°1'26″ = 1.53663067308 rad
Angle ∠ C = γ = 88.02438917143° = 88°1'26″ = 1.53663067308 rad

Height: ha = 28.98327534924
Height: hb = 1.99988105857
Height: hc = 1.99988105857

Median: ma = 28.98327534924
Median: mb = 14.56988022843
Median: mc = 14.56988022843

Inradius: r = 0.96660917831
Circumradius: R = 14.50986283852

Vertex coordinates: A[29; 0] B[0; 0] C[0.06989655172; 1.99988105857]
Centroid: CG[9.69896551724; 0.66662701952]
Coordinates of the circumscribed circle: U[14.5; 0.55002975305]
Coordinates of the inscribed circle: I[1; 0.96660917831]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176.0487783429° = 176°2'52″ = 0.06989791919 rad
∠ B' = β' = 91.97661082857° = 91°58'34″ = 1.53663067308 rad
∠ C' = γ' = 91.97661082857° = 91°58'34″ = 1.53663067308 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 = 2 ; ; b = 29 ; ; c = 29 ; ;

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

p = a+b+c = 2+29+29 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-2)(30-29)(30-29) } ; ; T = sqrt{ 840 } = 28.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 28.98 }{ 2 } = 28.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 28.98 }{ 29 } = 2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 28.98 }{ 29 } = 2 ; ;

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{ 2**2-29**2-29**2 }{ 2 * 29 * 29 } ) = 3° 57'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 29**2-2**2-29**2 }{ 2 * 2 * 29 } ) = 88° 1'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 29**2-2**2-29**2 }{ 2 * 29 * 2 } ) = 88° 1'26" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 28.98 }{ 30 } = 0.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 3° 57'8" } = 14.51 ; ;




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