Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and c (as equilateral triangle).

Equilateral triangle.

Sides: a = 48   b = 48   c = 48

Area: T = 997.661126516
Perimeter: p = 144
Semiperimeter: s = 72

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

Height: ha = 41.56992193817
Height: hb = 41.56992193817
Height: hc = 41.56992193817

Median: ma = 41.56992193817
Median: mb = 41.56992193817
Median: mc = 41.56992193817

Inradius: r = 13.85664064606
Circumradius: R = 27.71328129211

Vertex coordinates: A[48; 0] B[0; 0] C[24; 41.56992193817]
Centroid: CG[24; 13.85664064606]
Coordinates of the circumscribed circle: U[24; 13.85664064606]
Coordinates of the inscribed circle: I[24; 13.85664064606]

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 and c (as equilateral triangle).

a = 48 ; ; b = 48 ; ; c = 48 ; ;

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

p = a+b+c = 48+48+48 = 144 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 144 }{ 2 } = 72 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 72 * (72-48)(72-48)(72-48) } ; ; T = sqrt{ 995328 } = 997.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 997.66 }{ 48 } = 41.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 997.66 }{ 48 } = 41.57 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 997.66 }{ 48 } = 41.57 ; ;

6. 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{ 48**2+48**2-48**2 }{ 2 * 48 * 48 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 48**2+48**2-48**2 }{ 2 * 48 * 48 } ) = 60° ; ; gamma = 180° - alpha - beta = 180° - 60° - 60° = 60° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 997.66 }{ 72 } = 13.86 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 48 }{ 2 * sin 60° } = 27.71 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 48**2+2 * 48**2 - 48**2 } }{ 2 } = 41.569 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 48**2+2 * 48**2 - 48**2 } }{ 2 } = 41.569 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 48**2+2 * 48**2 - 48**2 } }{ 2 } = 41.569 ; ;
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