You hang a sign at the midpoint which is 1 m of a stiff mass

You hang a sign at the midpoint, which is 1 m, of a stiff, massless rod and decide to support it with a diagonal wire. The screw that holds the wire to the wall can withstand a max force of 76 N. How small can ? be, in degrees, and still support a sign with a mass of 10 kg so that the screw doesn\'t pop out of the wall?

Force exerted by sign = on screw when angle = = mgcos() 10*9.8cos() = 98 cos() N

Hence under min , 98 cos(_min) = 76;