0.15 0.15 0.15 triangle

Equilateral triangle.

Sides: a = 0.15   b = 0.15   c = 0.15

Area: T = 0.01097427858
Perimeter: p = 0.45
Semiperimeter: s = 0.225

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

Height: ha = 0.13299038106
Height: hb = 0.13299038106
Height: hc = 0.13299038106

Median: ma = 0.13299038106
Median: mb = 0.13299038106
Median: mc = 0.13299038106

Inradius: r = 0.04333012702
Circumradius: R = 0.08766025404

Vertex coordinates: A[0.15; 0] B[0; 0] C[0.075; 0.13299038106]
Centroid: CG[0.075; 0.04333012702]
Coordinates of the circumscribed circle: U[0.075; 0.04333012702]
Coordinates of the inscribed circle: I[0.075; 0.04333012702]

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?

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

p = a+b+c = 0.15+0.15+0.15 = 0.45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 0.45 }{ 2 } = 0.23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.23 * (0.23-0.15)(0.23-0.15)(0.23-0.15) } ; ; T = sqrt{ 0 } = 0.01 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.01 }{ 0.15 } = 0.13 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.01 }{ 0.15 } = 0.13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.01 }{ 0.15 } = 0.13 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 0.15**2+0.15**2-0.15**2 }{ 2 * 0.15 * 0.15 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 0.15**2+0.15**2-0.15**2 }{ 2 * 0.15 * 0.15 } ) = 60° ; ; gamma = 180° - alpha - beta = 180° - 60° - 60° = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.01 }{ 0.23 } = 0.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 0.15 }{ 2 * sin 60° } = 0.09 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.15**2+2 * 0.15**2 - 0.15**2 } }{ 2 } = 0.13 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.15**2+2 * 0.15**2 - 0.15**2 } }{ 2 } = 0.13 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.15**2+2 * 0.15**2 - 0.15**2 } }{ 2 } = 0.13 ; ;
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