75 75 75 triangle

Equilateral triangle.

Sides: a = 75   b = 75   c = 75

Area: T = 2435.696644814
Perimeter: p = 225
Semiperimeter: s = 112.5

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

Height: ha = 64.95219052838
Height: hb = 64.95219052838
Height: hc = 64.95219052838

Median: ma = 64.95219052838
Median: mb = 64.95219052838
Median: mc = 64.95219052838

Inradius: r = 21.65106350946
Circumradius: R = 43.30112701892

Vertex coordinates: A[75; 0] B[0; 0] C[37.5; 64.95219052838]
Centroid: CG[37.5; 21.65106350946]
Coordinates of the circumscribed circle: U[37.5; 21.65106350946]
Coordinates of the inscribed circle: I[37.5; 21.65106350946]

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 = 75 ; ; b = 75 ; ; c = 75 ; ;

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

p = a+b+c = 75+75+75 = 225 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 225 }{ 2 } = 112.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 112.5 * (112.5-75)(112.5-75)(112.5-75) } ; ; T = sqrt{ 5932617.19 } = 2435.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2435.7 }{ 75 } = 64.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2435.7 }{ 75 } = 64.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2435.7 }{ 75 } = 64.95 ; ;

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{ 75**2-75**2-75**2 }{ 2 * 75 * 75 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 75**2-75**2-75**2 }{ 2 * 75 * 75 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 75**2-75**2-75**2 }{ 2 * 75 * 75 } ) = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2435.7 }{ 112.5 } = 21.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 75 }{ 2 * sin 60° } = 43.3 ; ;




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