Equilateral triangle calculator (a)

Please enter one property of the equilateral triangle

Use symbols: a, h, T, p, r, R


You have entered side a.

Equilateral triangle.

Sides: a = 1820   b = 1820   c = 1820

Area: T = 1434311.274375
Perimeter: p = 5460
Semiperimeter: s = 2730

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

Height: ha = 1576.166623489
Height: hb = 1576.166623489
Height: hc = 1576.166623489

Median: ma = 1576.166623489
Median: mb = 1576.166623489
Median: mc = 1576.166623489

Inradius: r = 525.3898744963
Circumradius: R = 1050.777748993

Vertex coordinates: A[1820; 0] B[0; 0] C[910; 1576.166623489]
Centroid: CG[910; 525.3898744963]
Coordinates of the circumscribed circle: U[910; 525.3898744963]
Coordinates of the inscribed circle: I[910; 525.3898744963]

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. Input data entered: side a

a = 1820 ; ;

2. From side a we calculate b,c:

b = c = a = 1820 ; ;


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 = 1820 ; ; b = 1820 ; ; c = 1820 ; ;

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

p = a+b+c = 1820+1820+1820 = 5460 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 5460 }{ 2 } = 2730 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2730 * (2730-1820)(2730-1820)(2730-1820) } ; ; T = sqrt{ 2.057 * 10**{ 12 } } = 1434311.27 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1434311.27 }{ 1820 } = 1576.17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1434311.27 }{ 1820 } = 1576.17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1434311.27 }{ 1820 } = 1576.17 ; ;

7. 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{ 1820**2-1820**2-1820**2 }{ 2 * 1820 * 1820 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1820**2-1820**2-1820**2 }{ 2 * 1820 * 1820 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1820**2-1820**2-1820**2 }{ 2 * 1820 * 1820 } ) = 60° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1434311.27 }{ 2730 } = 525.39 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1820 }{ 2 * sin 60° } = 1050.78 ; ;




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