On 30 December in DR position LAT 28°24.0'S, LONG 32°15.0'W, you take an ex- meridian observation of the Sun's lower limb. The chronometer time of the sight is 02h 09m 16s, and the chronometer error is 00m 00s. The sextant altitude (hs) is 84°03.3'. The index error is 3.5' off the arc, and your height of eye is 62.0 feet. What is the latitude at meridian transit?

Correct Answer: Option B — LAT 28°51.9'S

Ex-meridian observations require applying the reduction to the meridian (reduction to the meridian formula) to the observed altitude. By calculating the time difference from local apparent noon and applying the correction factor based on the observer's latitude and the Sun's declination, the resulting latitude at meridian transit is 28°51.9'S.