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 = 200   b = 200   c = 200

Area: T = 17320.50880757
Perimeter: p = 600
Semiperimeter: s = 300

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

Height: ha = 173.2055080757
Height: hb = 173.2055080757
Height: hc = 173.2055080757

Median: ma = 173.2055080757
Median: mb = 173.2055080757
Median: mc = 173.2055080757

Inradius: r = 57.7355026919
Circumradius: R = 115.4770053838

Vertex coordinates: A[200; 0] B[0; 0] C[100; 173.2055080757]
Centroid: CG[100; 57.7355026919]
Coordinates of the circumscribed circle: U[100; 57.7355026919]
Coordinates of the inscribed circle: I[100; 57.7355026919]

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 = 200 ; ; b = 200 ; ; c = 200 ; ;

2. From we calculate b,c:

b = c = a = 200 ; ;


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 = 200 ; ; b = 200 ; ; c = 200 ; ; : Nr. 1

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

p = a+b+c = 200+200+200 = 600 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 600 }{ 2 } = 300 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 300 * (300-200)(300-200)(300-200) } ; ; T = sqrt{ 300000000 } = 17320.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17320.51 }{ 200 } = 173.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17320.51 }{ 200 } = 173.21 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17320.51 }{ 200 } = 173.21 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 200**2+200**2-200**2 }{ 2 * 200 * 200 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 200**2+200**2-200**2 }{ 2 * 200 * 200 } ) = 60° ; ; gamma = 180° - alpha - beta = 180° - 60° - 60° = 60° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17320.51 }{ 300 } = 57.74 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 200 }{ 2 * sin 60° } = 115.47 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 200**2+2 * 200**2 - 200**2 } }{ 2 } = 173.205 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 200**2+2 * 200**2 - 200**2 } }{ 2 } = 173.205 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 200**2+2 * 200**2 - 200**2 } }{ 2 } = 173.205 ; ;
Calculate another triangle

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

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