Let's call the point on the Earth's surface where Jupiter is at the zenith as the "sub-Jupiter point".
The latitude of the sub-Jupiter point is equal to the declination of Jupiter. Therefore, latitude 17° 29' 55.9" N is the answer for the latitude. (This is true if the flattening of the Earth can be ignored which would introduce an error of a fraction of a degree.)
There are two methods of calculating the longitude of the sub-Jupiter point:
* Based on the known right ascension of Jupiter and the Greenwich Mean Sidereal Time (GMST, which can be calculated from the date and time), calculate the longitude where the meridian has the same right ascension as Jupiter.
The GMST can be calculated from a number of posts such as How to find Greenwich Mean Sideral Time?. If the GMST were 2 hour, then the meridian at 15 E longitude would be 3 hour right ascension, 15 W longitude would be at 1 hour right ascension, and so on. 371
(1 hour right ascension = 15 degrees of longitude.) The difference between GMST and Jupiter's right ascension (converted from hours to degrees as needed) gives the longitude of the sub-Jupiter point.
* Based on the observed altitude and/or azimuth of Jupiter, calculate how many degrees Jupiter is east or west of the meridian. This is the hour angle of Jupiter. Add the hour angle to the current longitude to get the longitude of the sub-Jupiter point.
The relationship between celestial coordinates (hour angle and declination) and horizon coordinates (altitude and azimuth) can be calculated using posts such as Translating a zenith position to the nadir. This formula from that page gives the hour angle H directly (positive to the west of the observer): $$\mathrm{tan}\ H = \frac {\mathrm{sin}\ A}{\mathrm{cos}\ A\ \mathrm{sin}\ \phi + \mathrm{tan}\ h\ \mathrm{cos}\ \phi }$$
where $\phi$ is the latitude (+ North, − South) in degrees, A is the azimuth in degrees, and h is the height of the object in degrees. Please note that azimuths in this formula are measured from the South heading East (90°) then North (180°) and West (270° = -90°).
If H were +30 degrees, then the sub-Jupiter longitude would be 30 degrees further west of the observer's longitude. 371