32 32 32 triangle

Equilateral triangle.

Sides: a = 32   b = 32   c = 32

Area: T = 443.4055006738
Perimeter: p = 96
Semiperimeter: s = 48

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

Height: ha = 27.71328129211
Height: hb = 27.71328129211
Height: hc = 27.71328129211

Median: ma = 27.71328129211
Median: mb = 27.71328129211
Median: mc = 27.71328129211

Inradius: r = 9.2387604307
Circumradius: R = 18.47552086141

Vertex coordinates: A[32; 0] B[0; 0] C[16; 27.71328129211]
Centroid: CG[16; 9.2387604307]
Coordinates of the circumscribed circle: U[16; 9.2387604307]
Coordinates of the inscribed circle: I[16; 9.2387604307]

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 = 32+32+32 = 96 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 96 }{ 2 } = 48 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 48 * (48-32)(48-32)(48-32) } ; ; T = sqrt{ 196608 } = 443.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 443.41 }{ 32 } = 27.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 443.41 }{ 32 } = 27.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 443.41 }{ 32 } = 27.71 ; ;

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{ 32**2+32**2-32**2 }{ 2 * 32 * 32 } ) = 60° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 32**2+32**2-32**2 }{ 2 * 32 * 32 } ) = 60° ; ; gamma = 180° - alpha - beta = 180° - 60° - 60° = 60° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 443.41 }{ 48 } = 9.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 32 }{ 2 * sin 60° } = 18.48 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 32**2+2 * 32**2 - 32**2 } }{ 2 } = 27.713 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 32**2+2 * 32**2 - 32**2 } }{ 2 } = 27.713 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 32**2+2 * 32**2 - 32**2 } }{ 2 } = 27.713 ; ;
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