Stígurinn að fossinum er lengstur.

The forms you would usually look up are:

• stígur = path / trail
• foss = waterfall
• langur = long

The sentence uses inflected forms of these:

• stígurinn = the path
• fossinum = a case form of foss
• lengstur = the superlative form of langur

Because Icelandic usually adds the definite article to the end of the noun instead of using a separate word like English the.

So:

• stígur = a path
• stígurinn = the path

This attached article is extremely common in Icelandic.

Because the preposition að takes the dative case in this meaning.

The noun foss is masculine, and its singular forms include:

• foss = nominative
• fossi = dative
• fossinum = dative definite, to the waterfall

So að fossinum is the correct form here.

It is the same spelling, but not the same function.

Here, að is a preposition followed by a noun phrase:

• að fossinum = to the waterfall

In a phrase like að fara, að is the infinitive marker:

• að fara = to go

So learners need to recognize which job að is doing from the context.

It modifies stígurinn, not er.

So the structure is:

• Stígurinn að fossinum = the path to the waterfall
• er lengstur = is longest / is the longest

In other words, að fossinum helps identify which path we are talking about.

Because lengstur is the superlative of langur.

The pattern is:

• langur = long
• lengri = longer
• lengstur = longest

Notice that the vowel changes from a to e, so this is not completely regular from an English learner’s point of view.

Because the adjective is being used predicatively after er.

In Icelandic, the strong superlative form is commonly used in predicate position:

• Stígurinn er lengstur.

But when the adjective is directly attached to a definite noun, you often get the weak form:

• lengsti stígurinn = the longest path

So:

• er lengstur = predicate use
• lengsti stígurinn = attributive use

Adjectives in Icelandic agree with the noun they describe in gender, number, and case.

Here, stígurinn is:

• masculine
• singular
• nominative

So the adjective also appears in the matching form:

• lengstur

That agreement is an important part of Icelandic grammar.

Because Icelandic does not always express definiteness the same way English does.

English says:

• the longest

But Icelandic can simply say:

• lengstur

especially when the adjective is in predicate position after er and the context already makes the comparison clear.

So the idea of the longest is still there, even without a separate word before the adjective.

Yes. A superlative normally means that this path is being compared with other relevant paths.

The sentence does not have to say exactly what the comparison group is if it is already understood from context. For example, it could mean the longest:

• of several paths in the area
• of all the paths to that place
• of the paths being discussed

If you want to make the comparison explicit, Icelandic can do that too, for example with af plus a phrase meaning of/from all the paths.