A uniform board is leaning against a smooth vertical wall. Find torque

[leezak]

A uniform board is leaning against a smooth vertical wall. The board is at an angle above the horizontal ground. The coefficient of static friction between the ground and the lower end of the board is 0.350. Find the smallest value for the angle , such that the lower end of the board does not slide along the ground.

i drew a diagram and all the forces and then i found out that the sum of the y-axis forces are normal force= (m)(g)(sin(theta)) and that the sum of the x forces are (m)(g)(cos(theta))=normal force(.350) i then plugged the normal (m)(g)(sin(theta)) from the first equation into where the normal force is in the second equation to get (m)(g)cos(theta)=(m)(g)(sin(theta))(.6) then i canceled out the mg and solved for theta to get 70.71 degrees but that's the wrong answer... what am i doing wrong?

 

[WalterContrata]

Good approach, but I think you are a little off. If the ladder is not moving, the sum of the forces in any direction must be zero. In particular, the sum of the forces in the y direction must be zero. Which forces have components in the y direction, and what are their magnitudes?

Hope this helps.