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 = 1505   b = 1505   c = 1505

Area: T = 980784.5955103
Perimeter: p = 4515
Semiperimeter: s = 2257.5

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

Height: ha = 1303.36882327
Height: hb = 1303.36882327
Height: hc = 1303.36882327

Median: ma = 1303.36882327
Median: mb = 1303.36882327
Median: mc = 1303.36882327

Inradius: r = 434.4566077565
Circumradius: R = 868.912215513

Vertex coordinates: A[1505; 0] B[0; 0] C[752.5; 1303.36882327]
Centroid: CG[752.5; 434.4566077565]
Coordinates of the circumscribed circle: U[752.5; 434.4566077565]
Coordinates of the inscribed circle: I[752.5; 434.4566077565]

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

Calculate another triangle




How did we calculate this triangle?

1. Input data entered: side a b c (as equilateral triangle)

a = 1505 ; ; b = 1505 ; ; c = 1505 ; ;

2. From we calculate b,c:

b = c = a = 1505 ; ;


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 = 1505 ; ; b = 1505 ; ; c = 1505 ; ; : Nr. 1

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

p = a+b+c = 1505+1505+1505 = 4515 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 4515 }{ 2 } = 2257.5 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2257.5 * (2257.5-1505)(2257.5-1505)(2257.5-1505) } ; ; T = sqrt{ 961938421992 } = 980784.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 980784.6 }{ 1505 } = 1303.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 980784.6 }{ 1505 } = 1303.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 980784.6 }{ 1505 } = 1303.37 ; ;

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{ 1505**2-1505**2-1505**2 }{ 2 * 1505 * 1505 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1505**2-1505**2-1505**2 }{ 2 * 1505 * 1505 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1505**2-1505**2-1505**2 }{ 2 * 1505 * 1505 } ) = 60° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 980784.6 }{ 2257.5 } = 434.46 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1505 }{ 2 * sin 60° } = 868.91 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.