Mechanics Help

Hi,

I had some trouble with the following question:


How do they get the distances? I get its the perpendicular distance from X, but I don't understand how they worked that out.

Any help is appreciated!

For the first one,
a*cos(theta)
Is the horizontal distance from the bottom left "RF origin" (where the force W is perpendicular). This is the same axis where F is pointing. This is also the same from X by projecting the force W upwards rather than downwards (and again considering the horizontal distance from X where the force is perpendicular).

The others are similar. The ladder is length 2a and you use sin / cos to work out the vertical and horizontal distance from X.