8 8 8 triangle

Equilateral triangle.

Sides: a = 8   b = 8   c = 8

Area: T = 27.71328129211
Perimeter: p = 24
Semiperimeter: s = 12

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

Height: ha = 6.92882032303
Height: hb = 6.92882032303
Height: hc = 6.92882032303

Median: ma = 6.92882032303
Median: mb = 6.92882032303
Median: mc = 6.92882032303

Inradius: r = 2.30994010768
Circumradius: R = 4.61988021535

Vertex coordinates: A[8; 0] B[0; 0] C[4; 6.92882032303]
Centroid: CG[4; 2.30994010768]
Coordinates of the circumscribed circle: U[4; 2.30994010768]
Coordinates of the inscribed circle: I[4; 2.30994010768]

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 = 8 ; ; b = 8 ; ; c = 8 ; ;

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

p = a+b+c = 8+8+8 = 24 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 24 }{ 2 } = 12 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12 * (12-8)(12-8)(12-8) } ; ; T = sqrt{ 768 } = 27.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 27.71 }{ 8 } = 6.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 27.71 }{ 8 } = 6.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 27.71 }{ 8 } = 6.93 ; ;

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**2+8**2-8**2 }{ 2 * 8 * 8 } ) = 60° ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8**2+8**2-8**2 }{ 2 * 8 * 8 } ) = 60° ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 8**2+8**2-8**2 }{ 2 * 8 * 8 } ) = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 27.71 }{ 12 } = 2.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 60° } = 4.62 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8**2+2 * 8**2 - 8**2 } }{ 2 } = 6.928 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 8**2+2 * 8**2 - 8**2 } }{ 2 } = 6.928 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8**2+2 * 8**2 - 8**2 } }{ 2 } = 6.928 ; ;
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