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 = 52865286   b = 52865286   c = 52865286

Area: T = 1.21015725332E+15
Perimeter: p = 158595858
Semiperimeter: s = 79297929

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

Height: ha = 45782680.65443
Height: hb = 45782680.65443
Height: hc = 45782680.65443

Median: ma = 45782680.65443
Median: mb = 45782680.65443
Median: mc = 45782680.65443

Inradius: r = 15260893.55114
Circumradius: R = 30521787.10329

Vertex coordinates: A[52865286; 0] B[0; 0] C[26432643; 45782680.65443]
Centroid: CG[26432643; 15260893.55114]
Coordinates of the circumscribed circle: U[26432643; 15260893.55114]
Coordinates of the inscribed circle: I[26432643; 15260893.55114]

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 = 52865286 ; ; b = 52865286 ; ; c = 52865286 ; ;

2. From we calculate b,c:

b = c = a = 52865286 ; ;


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 = 52865286 ; ; b = 52865286 ; ; c = 52865286 ; ; : Nr. 1

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

p = a+b+c = 52865286+52865286+52865286 = 158595858 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 158595858 }{ 2 } = 79297929 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 79297929 * (79297929-52865286)(79297929-52865286)(79297929-52865286) } ; ; T = sqrt{ 1.464 * 10**{ 30 } } = 1.21 * 10**{ 15 } ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.21 * 10**{ 15 } }{ 52865286 } = 45782680.65 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.21 * 10**{ 15 } }{ 52865286 } = 45782680.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.21 * 10**{ 15 } }{ 52865286 } = 45782680.65 ; ;

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{ 52865286**2-52865286**2-52865286**2 }{ 2 * 52865286 * 52865286 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 52865286**2-52865286**2-52865286**2 }{ 2 * 52865286 * 52865286 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 52865286**2-52865286**2-52865286**2 }{ 2 * 52865286 * 52865286 } ) = 60° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.21 * 10**{ 15 } }{ 79297929 } = 15260893.55 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 52865286 }{ 2 * sin 60° } = 30521787.1 ; ;




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