
haarig
hairy
Covered with hair or made of hair.
Der Hund hat sehr haarige Pfoten.
The dog has very hairy paws.
hairy
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hairy
Covered with hair or made of hair.
Der Hund hat sehr haarige Pfoten.
The dog has very hairy paws.

tricky
Colloquial for a difficult, delicate, or complicated matter.
Das war eine ziemlich haarige Situation, aus der wir uns gerade noch retten konnten.
That was a pretty tricky situation that we just barely managed to get out of.
The adjective 'haarig' (hairy) is derived directly from the noun 'das Haar' (hair). The ending '-ig' is often used in German to form an adjective from a noun that means 'like' or 'full of' that noun.
Der neue Pullover ist von innen ganz weich und haarig.
The new sweater is completely soft and hairy on the inside.
You can recognize the figurative meaning 'schwierig' (difficult) by the fact that 'haarig' (hairy/tricky) describes an abstract noun. If it refers to a living being or an object, the literal meaning 'covered with hair' is usually meant.
Seine Brust war sehr haarig.
His chest was very hairy.
The meaning 'schwierig' (difficult) or 'heikel' (delicate/tricky) is colloquial. In formal or written contexts, you would more likely use words such as 'kompliziert' (complicated), 'schwierig' (difficult), or 'heikel' (delicate/tricky).
Aus dieser haarigen Situation kommen wir nur mit Glück wieder heraus.
We'll only get out of this tricky situation again with luck.
In the colloquial meaning, 'haarig' (tricky) is often combined with words such as 'Sache' (thing/matter), 'Angelegenheit' (matter), 'Situation' (situation), or 'Problem' (problem).
Die Reparatur des Motors ist eine haarige Angelegenheit.
Repairing the engine is a tricky matter.
hairy
Behaart and haarig can both express that a person or part of the body is covered with hair. Behaart describes this property in a factual way. Haarig often emphasizes the visible hairiness more strongly and can therefore sound more noticeable or evaluative.

Seine Arme sind auffällig dicht und haarig.
His arms are noticeably thickly covered with hair.
Seine Arme sind leicht behaart.
His arms are slightly hairy.