traurig
sad
Feeling or expressing a state of sorrow, suffering, or dejection.
Er war sehr traurig, als er von dem Unglück hörte.
He was very sad when he heard about the accident.

sad
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sad
Feeling or expressing a state of sorrow, suffering, or dejection.
Er war sehr traurig, als er von dem Unglück hörte.
He was very sad when he heard about the accident.

The adjective 'traurig' (sad) is closely related to the noun 'die Trauer' (grief, the deep pain over a loss) and the verb 'trauern' (to grieve). All of these words describe the state of sorrow.
Nach dem Tod ihres Hundes war ihre Trauer sehr groß.
After the death of her dog, her grief was very great.
To state the reason for the sadness, the preposition 'über' with the accusative is often used. The construction is: 'traurig sein über etwas' (to be sad about something).
Sie ist traurig über das schlechte Prüfungsergebnis.
She is sad about the poor exam result.
In colloquial language, 'traurig' (sad/pitiful) can also describe very poor quality or performance and then sounds disparaging. Here it means something like 'armselig' (pathetic) or 'erbärmlich' (miserable).
Fünf richtige Antworten von zwanzig sind ein trauriges Ergebnis.
Five correct answers out of twenty is a pitiful result.
It is easy to recognize whether a person has a feeling or a thing triggers a feeling. 'Jemand ist traurig' (someone is sad) describes a person. 'Etwas ist traurig' (something is sad), e.g. a story, describes a thing that makes people sad.
Der kleine Junge ist traurig, weil sein Spielzeug kaputt ist.
The little boy is sad because his toy is broken.
happy / lucky
'glücklich' and 'traurig' describe opposite feelings. Someone who is 'glücklich' feels joy, satisfaction, or well-being. Someone who is 'traurig' feels sorrow, pain, or dejection. The contrast is especially clear when talking about a person's mood. 'glücklich' fits good news, beautiful moments, or inner satisfaction; 'traurig' fits loss, disappointment, or bad news.

Am Wochenende bleibt er zu Hause, weil er nach dem Abschied noch traurig ist.
He is staying home this weekend because he is still sad after the farewell.
Das Kind ist glücklich, weil seine Eltern heute früher nach Hause kommen.
The child is happy because his parents are coming home earlier today.