3.5 3.5 3.5 triangle

Equilateral triangle.

Sides: a = 3.5   b = 3.5   c = 3.5

Area: T = 5.30444055982
Perimeter: p = 10.5
Semiperimeter: s = 5.25

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

Height: ha = 3.03110889132
Height: hb = 3.03110889132
Height: hc = 3.03110889132

Median: ma = 3.03110889132
Median: mb = 3.03110889132
Median: mc = 3.03110889132

Inradius: r = 1.01103629711
Circumradius: R = 2.02107259422

Vertex coordinates: A[3.5; 0] B[0; 0] C[1.75; 3.03110889132]
Centroid: CG[1.75; 1.01103629711]
Coordinates of the circumscribed circle: U[1.75; 1.01103629711]
Coordinates of the inscribed circle: I[1.75; 1.01103629711]

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

Calculate another triangle




How did we calculate this triangle?

a = 3.5 ; ; b = 3.5 ; ; c = 3.5 ; ;

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

p = a+b+c = 3.5+3.5+3.5 = 10.5 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 10.5 }{ 2 } = 5.25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.25 * (5.25-3.5)(5.25-3.5)(5.25-3.5) } ; ; T = sqrt{ 28.14 } = 5.3 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5.3 }{ 3.5 } = 3.03 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5.3 }{ 3.5 } = 3.03 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5.3 }{ 3.5 } = 3.03 ; ;

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{ 3.5**2-3.5**2-3.5**2 }{ 2 * 3.5 * 3.5 } ) = 60° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 3.5**2-3.5**2-3.5**2 }{ 2 * 3.5 * 3.5 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.5**2-3.5**2-3.5**2 }{ 2 * 3.5 * 3.5 } ) = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5.3 }{ 5.25 } = 1.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.5 }{ 2 * sin 60° } = 2.02 ; ;




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