2 2 2 triangle

Equilateral triangle.

Sides: a = 2   b = 2   c = 2

Area: T = 1.73220508076
Perimeter: p = 6
Semiperimeter: s = 3

Angle ∠ A = α = 60° = 1.04771975512 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 60° = 1.04771975512 rad

Height: ha = 1.73220508076
Height: hb = 1.73220508076
Height: hc = 1.73220508076

Median: ma = 1.73220508076
Median: mb = 1.73220508076
Median: mc = 1.73220508076

Inradius: r = 0.57773502692
Circumradius: R = 1.15547005384

Vertex coordinates: A[2; 0] B[0; 0] C[1; 1.73220508076]
Centroid: CG[1; 0.57773502692]
Coordinates of the circumscribed circle: U[1; 0.57773502692]
Coordinates of the inscribed circle: I[1; 0.57773502692]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 120° = 1.04771975512 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 120° = 1.04771975512 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 = 2 ; ; c = 2 ; ;

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

p = a+b+c = 2+2+2 = 6 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 6 }{ 2 } = 3 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3 * (3-2)(3-2)(3-2) } ; ; T = sqrt{ 3 } = 1.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.73 }{ 2 } = 1.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.73 }{ 2 } = 1.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.73 }{ 2 } = 1.73 ; ;

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**2-2**2-2**2 }{ 2 * 2 * 2 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 2**2-2**2-2**2 }{ 2 * 2 * 2 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 2**2-2**2-2**2 }{ 2 * 2 * 2 } ) = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.73 }{ 3 } = 0.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2 }{ 2 * sin 60° } = 1.15 ; ;




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