900 900 900 triangle

Equilateral triangle.

Sides: a = 900   b = 900   c = 900

Area: T = 350740.2898533
Perimeter: p = 2700
Semiperimeter: s = 1350

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

Height: ha = 779.4232863406
Height: hb = 779.4232863406
Height: hc = 779.4232863406

Median: ma = 779.4232863406
Median: mb = 779.4232863406
Median: mc = 779.4232863406

Inradius: r = 259.8087621135
Circumradius: R = 519.6155242271

Vertex coordinates: A[900; 0] B[0; 0] C[450; 779.4232863406]
Centroid: CG[450; 259.8087621135]
Coordinates of the circumscribed circle: U[450; 259.8087621135]
Coordinates of the inscribed circle: I[450; 259.8087621135]

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?

a = 900 ; ; b = 900 ; ; c = 900 ; ;

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

p = a+b+c = 900+900+900 = 2700 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2700 }{ 2 } = 1350 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1350 * (1350-900)(1350-900)(1350-900) } ; ; T = sqrt{ 123018750000 } = 350740.29 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 350740.29 }{ 900 } = 779.42 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 350740.29 }{ 900 } = 779.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 350740.29 }{ 900 } = 779.42 ; ;

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{ 900**2-900**2-900**2 }{ 2 * 900 * 900 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 900**2-900**2-900**2 }{ 2 * 900 * 900 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 900**2-900**2-900**2 }{ 2 * 900 * 900 } ) = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 350740.29 }{ 1350 } = 259.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 900 }{ 2 * sin 60° } = 519.62 ; ;




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