No. I believe it would be "Tha an t-uisge-beatha sa muga".
"In the..." is mostly done by 'san' except for our old friends b, m, p, c and g, when it is 'sa' or before sl, sn, sr, sa, se, si, so, and su when it is "san t-". The plural is sna or sna h-
So: ann an/am = in a san/sa/san t- = in the
I'm sure they'll cover this later but see here: https://learngaelic.net/lg-beginners/jslessons/index.jsp?lesson=7#screen_1
Definite articles are another, and complex, kettle of fish, and depend on case and gender. See https://learngaelic.scot/beginners/beagairbheag/grammar/article/index.jsp for a brief intro and https://gaelicgrammar.org/~gaelic/mediawiki/index.php/Articles for an eye-glazingly detailed description.
Off the top of my head, I think it might be "anns a' mhuga" but please don't take my word for it.
It was normal to put whisky in a mug or cup - with the tea - if you did not want people to see you drinking. There used to be a big problem with alcoholism in Gaelic-speaking areas. Whilst this was socially acceptable for men, it wasn't for women, so a lot of tea was fortified.
They prefer to get you used to things in easy examples before they explain but I assume you want to know when it is an t-, as well as why.
The fully story has several bits, so here is the simplified version that only applies to the material covered so far in the course. (For anyone who does know more Gaelic, I am only covering the situation where it comes before a vowel, and only covering the nominative and accusative.)
You have met two versions of the article:
- the an that never causes lenition, used with masculine singular nouns
- the an that causes lenition if it can and then changes to a', used with feminine singular nouns
Well, the first of these adds a t before a vowel
- an t-uisge-beatha the water-of-life (masculine)
- an abhainn the river (feminine)
The historical explanation is that the t was part of this form of the article in the first place, and was simply dropped before a consonant, in exactly the same way that English a/an was originally an and the n was dropped before a consonant. Why we write it an t- instead of *ant is beyond me. More modern teaching, including Duolingo, counts it as part of the article, regardless of how it is written, whereas older books tend to treat it as a t that is added onto the noun for no obvious reason. D