5.5 5.5 5.5 triangle

Equilateral triangle.

Sides: a = 5.5   b = 5.5   c = 5.5

Area: T = 13.09986342322
Perimeter: p = 16.5
Semiperimeter: s = 8.25

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

Height: ha = 4.76331397208
Height: hb = 4.76331397208
Height: hc = 4.76331397208

Median: ma = 4.76331397208
Median: mb = 4.76331397208
Median: mc = 4.76331397208

Inradius: r = 1.58877132403
Circumradius: R = 3.17554264805

Vertex coordinates: A[5.5; 0] B[0; 0] C[2.75; 4.76331397208]
Centroid: CG[2.75; 1.58877132403]
Coordinates of the circumscribed circle: U[2.75; 1.58877132403]
Coordinates of the inscribed circle: I[2.75; 1.58877132403]

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

Calculate another triangle




How did we calculate this triangle?

a = 5.5 ; ; b = 5.5 ; ; c = 5.5 ; ;

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

p = a+b+c = 5.5+5.5+5.5 = 16.5 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16.5 }{ 2 } = 8.25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.25 * (8.25-5.5)(8.25-5.5)(8.25-5.5) } ; ; T = sqrt{ 171.57 } = 13.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13.1 }{ 5.5 } = 4.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13.1 }{ 5.5 } = 4.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13.1 }{ 5.5 } = 4.76 ; ;

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{ 5.5**2-5.5**2-5.5**2 }{ 2 * 5.5 * 5.5 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.5**2-5.5**2-5.5**2 }{ 2 * 5.5 * 5.5 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.5**2-5.5**2-5.5**2 }{ 2 * 5.5 * 5.5 } ) = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13.1 }{ 8.25 } = 1.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5.5 }{ 2 * sin 60° } = 3.18 ; ;

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