Ask her if she will go with us OR Ask her whether she will go with us (?) [duplicate]

Solution 1:

In general, if you're turning a question into a noun, whether tends to be preferred in formal use. So this includes your example plus, e.g.:

The discussion was about [whether climate change was an important issue].

The issue is [whether we need to act now].

In informal usage, if is also possible in these cases.

It's important to understand that 'whether' and 'if' are not always interchangeable. The word whether only has the meaning of "if ... or not" (though you can still use the formula whether ... or not for emphasis), so for example you can't use whether in this case:

If/*whether you decide to come, give me a call.

Another key difference is that whether can introduce an infinitive, whereas if can't (they're different parts of speech):

They couldn't decide whether/*if to come.

Solution 2:

Whether is used to emphasis that one has two alternatives to pick from. Merriam-Webster gives two definitions:

1. archaic : which one of the two 
2. archaic : whichever one of the two

In the saddle example, there are three alternative results: too high, too low or just perfect. It doesn't make much sense to check the saddle for being too high and not caring about too low.