Calculate Magnitude of Force, FAL, to Keep Ladder from Falling

[Swany]

The ladder has a length L and makes an angle of θ with respect to the vertical wall. You have a mass, my, and are a horizontal distance x from the wall. The ladder has a mass of mL. Because the wall is slick, and the ice on the floor is slick, the frictional forces acting on the ladder are negligible. Find a formula for the magnitude of the force that your friend must exert to keep the ladder from falling, in terms of the following variables: x, L, m, θ, φ. Then use the following values to get a number for FAL. FAL is th force applied at the base of the ladder at φ above the horizontal.
FAL=

θ = 25.2 degrees
φ = 17.640 degrees
x = 1.488 meters
L = 6.2 meters
my = 90.0 kg
mL = 28.80 kg

Find the magnitude of the normal force that the wall exerts on the ladder.
NWL =

Find the magnitude of the normal force that the floor exerts on the ladder.
NFL =



I set the axis of rotation at the center of mass of the ladder, eliminating the torque due to weight. My two
positive torques are torque due to Fal and torque due to the normal force of the wall on the ladder. My two negative
torques are torque due to you on ladder and torque due to
the normal force of the ice on the ladder.

 

[apelling]

You have three unknowns therefore you must find three equations. Since the set up is in equilibrium we know that the sum of forces in any direction is zero and that moments found around any pivot are zero.

If you resolve forces vertically and equate components this gives one equation. Resolving horizontal forces gives a second and your moments equation around any pivot gives a third. I would set the pivot at the point where the ladder rests against the wall, since this removes NWL (an unknown) from the equation. The forces vertically also don't include NWL.
This gives two equations with two unknowns which can be solved by the method of your choice. Either simultaneously or rearrange one and sub into the other to knock another unknown.