How Do Two Ladders Hinged Together Maintain Equilibrium?

[xduckksx]

Homework Statement

Two straight uniform ladders, AC and BC have equal weights. THey stand in equilibrium with their feet, A and b, on rough horizontal ground and their tops freely hinged at C. Angle CAB=60, angle CBA=30 and AB=l.

a)Find the vertical reactions at A and B.
b)Find the magnitude and direction of the force exerted on BC by AC.

Homework Equations

Taking moments about various points, moment=Fd

The Attempt at a Solution

The first part isn't too hard, taking moments about B allows me to resolve the vertical reaction at A, similarly for b.

However, the second part is annoying me. It's clear that the direction of the force is 30degrees below horizontal, however I can't get the value right.
Ignoring the second ladder, taking moments about A, you get a vertical weight force halfway up the ladder which gives a moment which is seen in the perpendicular force at the top of the ladder. But this doesn't give me the correct answer for F, which is W/2

 

[ehild]

Show your FBD and derivations in detail, please. Why are you sure in the direction of the force between the ladders? Did you count with the moment of the horizontal forces, too?

ehild