What a rising sign is
The rising sign, also called the Ascendant, is the sign that was on the eastern horizon at the place and time of birth. The horizon turns through all twelve signs in a day. The rising sign therefore changes about every two hours.
That is why a missing birth time leaves this one blank. The Sun sign can still be found on most dates. The Moon sign can still be found on days the Moon did not change. The rising sign cannot, because the horizon keeps moving.
Why the city is part of the answer
The city supplies latitude, longitude, and the time zone, including the daylight saving rule that applied on that date. The same clock time in two cities is not the same instant, and the horizon is not the same line. A birth recorded as 14:30 in Lahore and 14:30 in London points at two different skies.
A parent, a hospital record, or a birth certificate is the usual place to find the clock time. If the time is rounded to the hour, the rising sign can still jump, because two hours is the whole span of one sign on the horizon.
Where to check it
The rising sign calculator needs the date, the city, and the time. The Moon sign calculator is the next page if you have the time and want the Moon as well.