How Are These Members in Compression and Tension

[wahaj]

Homework Statement

I'm supposed to find the forces in each member and then determine whether they are in tension or compression. I got the magnitudes right but it seems my directions are wrong according to the book but I am confident that I did the question right. The diagram is part of a larger truss connected at point A and B so point A and B only have he forces shown in the free body diagram.

Homework Equations

statistical equilibrium equations

The Attempt at a Solution

Since the 600N external force is acting towards the right, then the horizontal component of force CB will act towards the left to balance everything out. This will result in the force CB facing towards point C. This means that member CB is in tension. Now since the vertical component of force CB is facing upwards force CA will act downwards to balance everything out which would result in member CA being in compression. But the book says that it is CA which is in tension and BC which is in compression. So who is right? Me or the book?

 

[haruspex]

the horizontal component of force CB will act towards the left to balance everything out. This will result in the force CB facing towards point C. This means that member CB is in tension.

No, that's backwards. The force in question is the force the member CB is applying at point C. If that force is towards C then it means the member C is under compression.
As you know, action and reaction are equal and opposite. If the force from CB on the joint C is acting from B towards C then the force from the joint C on member CB is acting from C towards B.