Angle at which a ladder begins to slip

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Homework Statement



Consider the ladder in the figure. Assume there is friction between the verticle wall and the ladder, with the coeffecient of static friction=0.30. Find the angle at which the ladder just begins to slip.

Homework Equations



[tex]\Sigma[/tex][tex]\tau[/tex]=0=NwLsin[tex]\Theta[/tex]-mg(L/2)sin(90-[tex]\Theta[/tex])
0=+NwLsin[tex]\Theta[/tex]-mg(L/2)cos[tex]\Theta[/tex]

[tex]\Sigma[/tex]Fx[/=0=-Nw+Ffriction
[tex]\Sigma[/tex]Fy=0=NF-mg

Ffriction=[tex]\mu[/tex]sNF=[tex]\mu[/tex]
smg

tan[tex]\Theta[/tex]=1/2[tex]\mu[/tex]s

The Attempt at a Solution



tan[tex]\Theta[/tex]=1/2(0.30)
tan-1(1.667)=[tex]\Theta[/tex]
59=[tex]\Theta[/tex]

I got 59 but the answer given by the book is 40
 
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