28 28 28 triangle

Equilateral triangle.

Sides: a = 28   b = 28   c = 28

Area: T = 339.4821958283
Perimeter: p = 84
Semiperimeter: s = 42

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

Height: ha = 24.2498711306
Height: hb = 24.2498711306
Height: hc = 24.2498711306

Median: ma = 24.2498711306
Median: mb = 24.2498711306
Median: mc = 24.2498711306

Inradius: r = 8.08329037687
Circumradius: R = 16.16658075373

Vertex coordinates: A[28; 0] B[0; 0] C[14; 24.2498711306]
Centroid: CG[14; 8.08329037687]
Coordinates of the circumscribed circle: U[14; 8.08329037687]
Coordinates of the inscribed circle: I[14; 8.08329037687]

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 = 28 ; ; b = 28 ; ; c = 28 ; ;

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

p = a+b+c = 28+28+28 = 84 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 84 }{ 2 } = 42 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 42 * (42-28)(42-28)(42-28) } ; ; T = sqrt{ 115248 } = 339.48 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 339.48 }{ 28 } = 24.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 339.48 }{ 28 } = 24.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 339.48 }{ 28 } = 24.25 ; ;

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{ 28**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 339.48 }{ 42 } = 8.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 28 }{ 2 * sin 60° } = 16.17 ; ;




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