There isn't a one-to-one correspondence between その and English words. Often it is best translated "that" and would be awkward or incorrect to translate it as "the", but there are also circumstances in which it is much more natural to translate it as "the" and where "that" feels less natural to me.
In an exercises like this there's not really enough context to know, so I think both are totally valid.
I think I agree with him. The word of "sono/kono/ano" is refer to the direction. So, the meaning of "sono menu" is "that menu" "the menu" should be "menu desu"
I'm still confused what the difference is between using "その" and ”それ”. Wouldn't they both mean the same thing in this sentence (The menu/That menu)? How would it change the meaning of this sentence if それ replaced その?
There is a big difference. Though they both mean the same thing when translated to English (I prefer translating it to 'that' because of how K-S-A-D words work in Japanese), they are used differently. As you can see from pariah_ls example, それ never has an noun following it, while その has to have a noun after it. You could think of それ as 'this one' and その as 'this X', replacing the X with the following noun. それ is actually a noun itself, while その is an adjective.
I hope this clears it up a bit.
This and the. No that. If I remember correctly, 'sono' is a word to indicate that I point to something closer to my speaking partner, therefore 'that' instead of 'the'.
I'm confused, really.