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 = 40   b = 40   c = 40

Area: T = 692.8220323028
Perimeter: p = 120
Semiperimeter: s = 60

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

Height: ha = 34.64110161514
Height: hb = 34.64110161514
Height: hc = 34.64110161514

Median: ma = 34.64110161514
Median: mb = 34.64110161514
Median: mc = 34.64110161514

Inradius: r = 11.54770053838
Circumradius: R = 23.09440107676

Vertex coordinates: A[40; 0] B[0; 0] C[20; 34.64110161514]
Centroid: CG[20; 11.54770053838]
Coordinates of the circumscribed circle: U[20; 11.54770053838]
Coordinates of the inscribed circle: I[20; 11.54770053838]

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?

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 = 40 ; ; b = 40 ; ; c = 40 ; ;

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

p = a+b+c = 40+40+40 = 120 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 120 }{ 2 } = 60 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 60 * (60-40)(60-40)(60-40) } ; ; T = sqrt{ 480000 } = 692.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 692.82 }{ 40 } = 34.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 692.82 }{ 40 } = 34.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 692.82 }{ 40 } = 34.64 ; ;

5. 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{ 40**2-40**2-40**2 }{ 2 * 40 * 40 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 40**2-40**2-40**2 }{ 2 * 40 * 40 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 40**2-40**2-40**2 }{ 2 * 40 * 40 } ) = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 692.82 }{ 60 } = 11.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 40 }{ 2 * sin 60° } = 23.09 ; ;




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