Equilateral triangle calculator (c)

Please enter one property of the equilateral triangle

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


You have entered side c.

Equilateral triangle.

Sides: a = 1.2   b = 1.2   c = 1.2

Area: T = 0.62435382907
Perimeter: p = 3.6
Semiperimeter: s = 1.8

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

Height: ha = 1.03992304845
Height: hb = 1.03992304845
Height: hc = 1.03992304845

Median: ma = 1.03992304845
Median: mb = 1.03992304845
Median: mc = 1.03992304845

Inradius: r = 0.34664101615
Circumradius: R = 0.6932820323

Vertex coordinates: A[1.2; 0] B[0; 0] C[0.6; 1.03992304845]
Centroid: CG[0.6; 0.34664101615]
Coordinates of the circumscribed circle: U[0.6; 0.34664101615]
Coordinates of the inscribed circle: I[0.6; 0.34664101615]

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 c

c = 1.2 ; ;

2. From we calculate b,c:

b = c = a = 1.2 ; ;
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 = 1.2 ; ; b = 1.2 ; ; c = 1.2 ; ;

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

p = a+b+c = 1.2+1.2+1.2 = 3.6 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 3.6 }{ 2 } = 1.8 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1.8 * (1.8-1.2)(1.8-1.2)(1.8-1.2) } ; ; T = sqrt{ 0.39 } = 0.62 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.62 }{ 1.2 } = 1.04 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.62 }{ 1.2 } = 1.04 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.62 }{ 1.2 } = 1.04 ; ;

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{ 1.2**2+1.2**2-1.2**2 }{ 2 * 1.2 * 1.2 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1.2**2+1.2**2-1.2**2 }{ 2 * 1.2 * 1.2 } ) = 60° ; ; gamma = 180° - alpha - beta = 180° - 60° - 60° = 60° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.62 }{ 1.8 } = 0.35 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1.2 }{ 2 * sin 60° } = 0.69 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.2**2+2 * 1.2**2 - 1.2**2 } }{ 2 } = 1.039 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.2**2+2 * 1.2**2 - 1.2**2 } }{ 2 } = 1.039 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.2**2+2 * 1.2**2 - 1.2**2 } }{ 2 } = 1.039 ; ;
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