In sewing language, "gusset" it's "cuchillo, cuchilla, nesga, escudete", a kind of triangular piece of a garment. If the sense is the mentioned by FD, litterally "profondeur" it's "profundidad", or "fondo" (of a concavity). "Profundidad" is employed mainly with measurements, for example:
"El submarino está a 200 metros de profundidad", or "la profundidad de este pozo es de 10 metros", or "la caja mide 50 cm de ancho X 100 de largo X 30 de profundidad".
Perhaps another synonymous can be "tiro" (in a pair of breeches), "hondura" ("en lo más hondo de mi corazón" = in the depth of my heart, my soul), or "calado" (in a ship).
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