71 71 71 triangle

Equilateral triangle.

Sides: a = 71   b = 71   c = 71

Area: T = 2182.817703024
Perimeter: p = 213
Semiperimeter: s = 106.5

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

Height: ha = 61.48878036687
Height: hb = 61.48878036687
Height: hc = 61.48878036687

Median: ma = 61.48878036687
Median: mb = 61.48878036687
Median: mc = 61.48878036687

Inradius: r = 20.49659345562
Circumradius: R = 40.99218691125

Vertex coordinates: A[71; 0] B[0; 0] C[35.5; 61.48878036687]
Centroid: CG[35.5; 20.49659345562]
Coordinates of the circumscribed circle: U[35.5; 20.49659345562]
Coordinates of the inscribed circle: I[35.5; 20.49659345562]

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 = 71 ; ; b = 71 ; ; c = 71 ; ;

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

p = a+b+c = 71+71+71 = 213 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 213 }{ 2 } = 106.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 106.5 * (106.5-71)(106.5-71)(106.5-71) } ; ; T = sqrt{ 4764690.19 } = 2182.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2182.82 }{ 71 } = 61.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2182.82 }{ 71 } = 61.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2182.82 }{ 71 } = 61.49 ; ;

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{ 71**2+71**2-71**2 }{ 2 * 71 * 71 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 71**2+71**2-71**2 }{ 2 * 71 * 71 } ) = 60° ; ; gamma = 180° - alpha - beta = 180° - 60° - 60° = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2182.82 }{ 106.5 } = 20.5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 71 }{ 2 * sin 60° } = 40.99 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 71**2+2 * 71**2 - 71**2 } }{ 2 } = 61.488 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 71**2+2 * 71**2 - 71**2 } }{ 2 } = 61.488 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 71**2+2 * 71**2 - 71**2 } }{ 2 } = 61.488 ; ;
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