2 28 28 triangle

Acute isosceles triangle.

Sides: a = 2   b = 28   c = 28

Area: T = 27.98221371593
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 4.09334261954° = 4°5'36″ = 0.07114437648 rad
Angle ∠ B = β = 87.95332869023° = 87°57'12″ = 1.53550744444 rad
Angle ∠ C = γ = 87.95332869023° = 87°57'12″ = 1.53550744444 rad

Height: ha = 27.98221371593
Height: hb = 1.99987240828
Height: hc = 1.99987240828

Median: ma = 27.98221371593
Median: mb = 14.07112472795
Median: mc = 14.07112472795

Inradius: r = 0.96549012814
Circumradius: R = 14.00989371219

Vertex coordinates: A[28; 0] B[0; 0] C[0.07114285714; 1.99987240828]
Centroid: CG[9.35771428571; 0.66662413609]
Coordinates of the circumscribed circle: U[14; 0.55003191829]
Coordinates of the inscribed circle: I[1; 0.96549012814]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 175.9076573805° = 175°54'24″ = 0.07114437648 rad
∠ B' = β' = 92.04767130977° = 92°2'48″ = 1.53550744444 rad
∠ C' = γ' = 92.04767130977° = 92°2'48″ = 1.53550744444 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 = 28 ; ; c = 28 ; ;

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

p = a+b+c = 2+28+28 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-2)(29-28)(29-28) } ; ; T = sqrt{ 783 } = 27.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 27.98 }{ 2 } = 27.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 27.98 }{ 28 } = 2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 27.98 }{ 28 } = 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**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 4° 5'36" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-2**2-28**2 }{ 2 * 2 * 28 } ) = 87° 57'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-2**2-28**2 }{ 2 * 28 * 2 } ) = 87° 57'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 27.98 }{ 29 } = 0.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 4° 5'36" } = 14.01 ; ;




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