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 = 58   b = 58   c = 58

Area: T = 1456.655472917
Perimeter: p = 174
Semiperimeter: s = 87

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

Height: ha = 50.22994734195
Height: hb = 50.22994734195
Height: hc = 50.22994734195

Median: ma = 50.22994734195
Median: mb = 50.22994734195
Median: mc = 50.22994734195

Inradius: r = 16.74331578065
Circumradius: R = 33.4866315613

Vertex coordinates: A[58; 0] B[0; 0] C[29; 50.22994734195]
Centroid: CG[29; 16.74331578065]
Coordinates of the circumscribed circle: U[29; 16.74331578065]
Coordinates of the inscribed circle: I[29; 16.74331578065]

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 = 58 ; ; b = 58 ; ; c = 58 ; ;

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

p = a+b+c = 58+58+58 = 174 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 174 }{ 2 } = 87 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 87 * (87-58)(87-58)(87-58) } ; ; T = sqrt{ 2121843 } = 1456.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1456.65 }{ 58 } = 50.23 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1456.65 }{ 58 } = 50.23 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1456.65 }{ 58 } = 50.23 ; ;

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{ 58**2-58**2-58**2 }{ 2 * 58 * 58 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 58**2-58**2-58**2 }{ 2 * 58 * 58 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 58**2-58**2-58**2 }{ 2 * 58 * 58 } ) = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1456.65 }{ 87 } = 16.74 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 58 }{ 2 * sin 60° } = 33.49 ; ;




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