When the fast of Tish'ah BeAb is over if there is a clear and unobstructed view of the moon, Birkath Hallebanah (the blessing on the moon) should be recited. However, since one has been fasting the whole day, it is appropriate to taste something before reciting the blessing since this blessing should be recited in happiness.
Since one did not do a complete Netilath Yadayim (ritual washing of the hands) that morning, but only did it up to the knuckles, one should do the complete Netilath Yadayim, till the wrists, before reciting Birkath Hallebanah.
(See Ben Ish Hai, 1st Year, Parashath Debarim, Oth 28)