Equilateral triangle calculator (a)

Please enter one property of the equilateral triangle

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


You have entered side a.

Equilateral triangle.

Sides: a = 30   b = 30   c = 30

Area: T = 389.7111431703
Perimeter: p = 90
Semiperimeter: s = 45

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

Height: ha = 25.98107621135
Height: hb = 25.98107621135
Height: hc = 25.98107621135

Median: ma = 25.98107621135
Median: mb = 25.98107621135
Median: mc = 25.98107621135

Inradius: r = 8.66602540378
Circumradius: R = 17.32105080757

Vertex coordinates: A[30; 0] B[0; 0] C[15; 25.98107621135]
Centroid: CG[15; 8.66602540378]
Coordinates of the circumscribed circle: U[15; 8.66602540378]
Coordinates of the inscribed circle: I[15; 8.66602540378]

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

a = 30 ; ;

2. From side a we calculate b,c:

b = c = a = 30 ; ;


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 = 30 ; ; b = 30 ; ; c = 30 ; ;

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

p = a+b+c = 30+30+30 = 90 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 90 }{ 2 } = 45 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 45 * (45-30)(45-30)(45-30) } ; ; T = sqrt{ 151875 } = 389.71 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 389.71 }{ 30 } = 25.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 389.71 }{ 30 } = 25.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 389.71 }{ 30 } = 25.98 ; ;

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{ 30**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 60° ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 389.71 }{ 45 } = 8.66 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 30 }{ 2 * sin 60° } = 17.32 ; ;




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