Equilateral triangle calculator

Please enter one property of the equilateral triangle

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


You have entered side a, b and c (as equilateral triangle).

Equilateral triangle.

Sides: a = 36.891   b = 36.891   c = 36.891

Area: T = 589.3076853061
Perimeter: p = 110.673
Semiperimeter: s = 55.33765

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

Height: ha = 31.9498543171
Height: hb = 31.9498543171
Height: hc = 31.9498543171

Median: ma = 31.9498543171
Median: mb = 31.9498543171
Median: mc = 31.9498543171

Inradius: r = 10.65495143903
Circumradius: R = 21.29990287807

Vertex coordinates: A[36.891; 0] B[0; 0] C[18.44655; 31.9498543171]
Centroid: CG[18.44655; 10.65495143903]
Coordinates of the circumscribed circle: U[18.44655; 10.65495143903]
Coordinates of the inscribed circle: I[18.44655; 10.65495143903]

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 b c (as equilateral triangle)

a = 36.891 ; ; b = 36.891 ; ; c = 36.891 ; ;

2. From we calculate b,c:

b = c = a = 36.891 ; ;


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 = 36.89 ; ; b = 36.89 ; ; c = 36.89 ; ;

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

p = a+b+c = 36.89+36.89+36.89 = 110.67 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 110.67 }{ 2 } = 55.34 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 55.34 * (55.34-36.89)(55.34-36.89)(55.34-36.89) } ; ; T = sqrt{ 347282.57 } = 589.31 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 589.31 }{ 36.89 } = 31.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 589.31 }{ 36.89 } = 31.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 589.31 }{ 36.89 } = 31.95 ; ;

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{ 36.89**2-36.89**2-36.89**2 }{ 2 * 36.89 * 36.89 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 36.89**2-36.89**2-36.89**2 }{ 2 * 36.89 * 36.89 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 36.89**2-36.89**2-36.89**2 }{ 2 * 36.89 * 36.89 } ) = 60° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 589.31 }{ 55.34 } = 10.65 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 36.89 }{ 2 * sin 60° } = 21.3 ; ;




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