8.08 8.08 8.08 triangle

Equilateral triangle.

Sides: a = 8.08   b = 8.08   c = 8.08

Area: T = 28.27698404608
Perimeter: p = 24.24
Semiperimeter: s = 12.12

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

Height: ha = 6.99774852626
Height: hb = 6.99774852626
Height: hc = 6.99774852626

Median: ma = 6.99774852626
Median: mb = 6.99774852626
Median: mc = 6.99774852626

Inradius: r = 2.33224950875
Circumradius: R = 4.66549901751

Vertex coordinates: A[8.08; 0] B[0; 0] C[4.04; 6.99774852626]
Centroid: CG[4.04; 2.33224950875]
Coordinates of the circumscribed circle: U[4.04; 2.33224950875]
Coordinates of the inscribed circle: I[4.04; 2.33224950875]

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?

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

p = a+b+c = 8.08+8.08+8.08 = 24.24 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24.24 }{ 2 } = 12.12 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.12 * (12.12-8.08)(12.12-8.08)(12.12-8.08) } ; ; T = sqrt{ 799.18 } = 28.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 28.27 }{ 8.08 } = 7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 28.27 }{ 8.08 } = 7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 28.27 }{ 8.08 } = 7 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 8.08**2+8.08**2-8.08**2 }{ 2 * 8.08 * 8.08 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8.08**2+8.08**2-8.08**2 }{ 2 * 8.08 * 8.08 } ) = 60° ; ;
 gamma = 180° - alpha - beta = 180° - 60° - 60° = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 28.27 }{ 12.12 } = 2.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8.08 }{ 2 * sin 60° } = 4.66 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.08**2+2 * 8.08**2 - 8.08**2 } }{ 2 } = 6.997 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.08**2+2 * 8.08**2 - 8.08**2 } }{ 2 } = 6.997 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.08**2+2 * 8.08**2 - 8.08**2 } }{ 2 } = 6.997 ; ;
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