A uniform ladder of mass (m = 14.5 kg) and length (L) leans against a frictionless wall, see figure. Find the static friction force between the ladder and the floor if the angle θ = 64.0°?

Answer 1

Ok, i misread my sketch.

summing vertical forces indicates the normal force at the ground is mg.

summing horizontal forces:
at the wall point, summing forces about the base point,
mg*L/2*cos64-Fwall*L*sin64=0
Fwall=.5mg*ctn64

Now, summing horizotal forces
.5mgctn64-Ffriction=
.5mg ctn64=mu*mg
mu=.5*cotan 64

check that.

Answer 2

No sir I have tried .243 did not work.

The ladder is against a wall/floor that makes the shape of a backwards L if that makes sense.