Az úszómester megnézi a mélységet.

Hungarian has two forms of the definite article: a and az. They both mean the.

• Use az before a vowel sound: az úszómester
• Use a before a consonant sound: a mélységet

So the choice is based on pronunciation, not on meaning or gender.

Úszómester is a compound word:

• úszó = swimmer / swimming
• mester = master

But as a whole, úszómester means lifeguard or pool attendant, not literally swimming master in normal English. In many contexts it suggests the person supervising a swimming pool.

Because it is the direct object of the verb.

The base noun is mélység, meaning depth. Hungarian marks many direct objects with the accusative ending -t. After some stems, a linking vowel appears before that -t, so:

• mélység
  • -et → mélységet

So a mélységet means the depth as the thing being checked.

Nézi means looks at, watches, or is looking at.
Megnézi usually means looks at and checks, takes a look at, or examines.

The prefix meg- often adds a sense of completion or a definite, bounded action. So in this sentence, megnézi is more natural than nézi if the idea is that the lifeguard checks the depth.

It shows that the verb is in the definite conjugation.

Hungarian verbs often have two sets of endings:

• indefinite conjugation, used when there is no definite object
• definite conjugation, used when there is a definite object

Here the object is a mélységet = the depth, which is definite, so the verb is megnézi.

Compare:

• megnéz valamit = he/she checks something
• megnézi a mélységet = he/she checks the depth

In this sentence:

• az úszómester is the subject
• a mélységet is the object

A big clue is the ending -t on mélységet, which marks it as the direct object. Hungarian often uses case endings like this, so word order can be more flexible than in English.

This sentence has a neutral, natural word order:

Az úszómester megnézi a mélységet.

Very roughly, it is subject + verb + object. But Hungarian word order is more flexible than English, and changing it often changes the emphasis.

For example, if you move a mélységet forward, you emphasize the depth. So the basic meaning can stay similar, but the focus changes.

A rough English-style guide is:

az OO-soh-mesh-ter meg-NAY-zee a MAYY-shay-get

A few useful pronunciation points:

• sz = English s
• s = English sh
• ly is pronounced like y in modern Hungarian
• stress is on the first syllable of each word

So:

• úszómester ≈ OO-soh-mesh-ter
• megnézi ≈ meg-NAY-zee
• mélységet ≈ MAYY-shay-get

Yes, very much. In Hungarian, accents are not optional spelling marks. They show important vowel differences, especially vowel length.

For example:

• u and ú are different
• e and é are different
• o and ó are different

So you should learn and write the accented forms correctly: úszómester, megnézi, mélységet.

Not always exactly. Úszómester often suggests a lifeguard or supervising staff member at a swimming pool. Another Hungarian word, vízimentő, is closer to water rescuer or a more general rescue lifeguard.

So úszómester is a good translation here, but like many job titles, the exact nuance depends on context.