[Don José]

Wellcome.

"Hacha" is a femenine word, but we use "un" or "el" for phonetics reasons. "La hacha" or "una hacha" sound bad because the repetition of the "a" and the fact that the accent of "hacha" is on the first "a".

so, it could be correct to write or speak : "la águila", for example.

Correct, but not frequent. Here you are a whole explanation about this subject:

http://www.rae.es/rae/gestores/gespub000018.nsf/%28voAnexos%29/arch8100821B76809110C12571B80038BA4A/$File/CuestionesparaelFAQdeconsultas.htm#ap10