Puella sutorem rogat utrum soleae hae satis firmae sint ad longum iter.

Because rogat takes a direct object: the person being asked.

• puella = the girl, nominative singular, the subject
• sutorem = the shoemaker/cobbler, accusative singular, the object of rogat

So Puella sutorem rogat means The girl asks the shoemaker.

In English we often say asks him whether..., and Latin works similarly: the person asked is treated as the direct object.

It introduces an indirect question, specifically a yes/no indirect question.

The girl is not directly saying Are these sandals... ?
Instead, the sentence reports the question indirectly:

• direct question: Utrum soleae hae satis firmae sunt...?
• indirect question after rogat: utrum soleae hae satis firmae sint...

So utrum here means whether.

Utrum is a common way to introduce a yes/no question, especially an indirect one meaning whether.

In this sentence, the girl is asking whether the sandals are sturdy enough.

A few useful points:

• utrum can introduce a simple yes/no question
• it can also appear in a pair: utrum ... an ... = whether ... or ...
• here there is no explicit or not, so utrum alone is enough

So utrum is functioning very naturally as whether.

Because in Latin, indirect questions normally take the subjunctive.

So although English says whether these sandals are sturdy enough, Latin uses:

• sint = present subjunctive of esse

This is not because the speaker doubts the fact in some special way; it is simply standard grammar for an indirect question.

Compare:

• direct: Soleae hae satis firmae sunt? = Are these sandals sturdy enough?
• indirect: rogat utrum soleae hae satis firmae sint = she asks whether these sandals are sturdy enough

It is present because of the normal sequence of tenses.

The main verb is rogat = asks, a present-tense verb.
The subordinate verb describes something happening at the same time as the asking, so Latin uses the present subjunctive:

• rogat ... sint = she asks whether they are

If the main verb were past, Latin would usually shift accordingly:

• rogavit utrum ... essent = she asked whether they were

Both orders are possible in Latin.

Latin word order is more flexible than English because case endings show the grammatical relationships. So:

• soleae hae
• hae soleae

can both mean these sandals.

The choice of order often depends on emphasis, rhythm, or style. In soleae hae, the noun comes first and the demonstrative follows, which can slightly spotlight or point out the sandals already under discussion: these sandals here.

Because it agrees with soleae.

• soleae is feminine plural nominative
• hae is the nominative feminine plural form of hic, haec, hoc

So soleae hae means these sandals.

Latin adjectives and demonstratives must agree with the nouns they modify in:

• gender
• number
• case

Because it is an adjective describing soleae.

• soleae = feminine plural nominative
• firmae = feminine plural nominative of firmus, -a, -um

So soleae hae satis firmae means these sandals [are] sufficiently sturdy.

The adjective agrees with the noun just like hae does.

Satis is an indeclinable adverb meaning enough or sufficiently.

Here it modifies firmae:

• satis firmae = firm enough, sturdy enough

So the idea is not just that the sandals are sturdy, but that they are sturdy to a sufficient degree.

Ad with the accusative often expresses purpose, goal, or fitness for something.

Here:

• ad = for
• longum iter = a long journey

So satis firmae sint ad longum iter means are sturdy enough for a long journey.

This is a very common Latin pattern:

• idoneus ad = suitable for
• aptus ad = fit for
• and similarly here, something is sturdy enough ad some purpose

Iter is accusative singular because it follows ad, which takes the accusative.

• nominative: iter = journey
• accusative: iter again, because this is a neuter noun of the third declension

That is why the form looks the same.

Longum is also accusative singular neuter, agreeing with iter:

• longum iter = a long journey

So even though iter looks unchanged, it is accusative because of ad.

Iter, itineris is a third-declension neuter noun meaning journey, march, or route.

It belongs to a small group of neuter nouns in -er such as:

• iter, itineris
• opus, operis is different in form, but another common neuter third-declension noun
• iecur, iecinoris is another irregular one

For this sentence, the key thing is:

• dictionary form: iter, itineris
• here: iter = accusative singular after ad

Sometimes Latin can introduce an indirect yes/no question without utrum, but utrum is clear and very common.

With verbs of asking, knowing, seeing, and so on, Latin often uses an explicit interrogative marker:

• rogat utrum...
• quaerit num...
• nescio an... in some contexts

Here utrum cleanly signals whether and avoids ambiguity.

Here it means asks in the sense of inquires of someone.

That is important because rogare can have more than one use:

• aliquem rogare = to ask someone
• aliquid rogare = to ask something
• aliquem aliquid rogare = to ask someone something

In this sentence, the girl asks the shoemaker whether the sandals are sturdy enough. So the structure is:

• sutorem = the person asked
• utrum ... sint = what she asks, in the form of an indirect question

Because this is not a that-clause in Latin; it is an indirect question.

English distinguishes:

• She says that the sandals are sturdy enough
• She asks whether the sandals are sturdy enough

Latin also distinguishes those ideas. After rogat, Latin does not use an accusative-and-infinitive here; it uses an indirect question:

• rogat utrum ... sint

So whether is the right connector, not that.