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30-60-90 Triangle

Definition

Defining inequalities

y>=0 and sqrt(3) a>=2 (sqrt(3) x + y) and x>=0

Lamina properties

(0, 0) | (a/2, 0) | (0, (sqrt(3) a)/2)

a>0

(data not available)

(sqrt(3) a)/2

A = (sqrt(3) a^2)/8

x^_ = (a/6, a/(2 sqrt(3)))

Mechanical properties

J_x invisible comma x = (sqrt(3) a^4)/64

J_y invisible comma y = a^4/(64 sqrt(3))

J_zz = a^4/(16 sqrt(3))

J_x invisible comma y = -a^4/128

r_x = a/(2 sqrt(2))
r_y = a/(2 sqrt(6))

Distance properties

a/2 | a | (sqrt(3) a)/2

p = 1/2 (3 + sqrt(3)) a

r = 1/4 (sqrt(3) - 1) a

R = a/2

χ = 1

s^_ = (a (204 + 36 sqrt(3) + 81 log(3) + 2 (9 + 8 sqrt(3)) log(2 + sqrt(3))))/1440

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