On 16 June in DR position LAT 50°57.0'S, LONG 53°03.9'W (ZD+4), you take an ex-meridian observation of Acrux at lower transit. The chronometer time of the sight is 10h 08m 18s, and the chronometer error is 02m 12s fast. The sextant altitude (hs) is 23°49.0'. The index error is 1.1' off the arc, and your height of eye is 26 feet. What is the latitude at meridian transit?

Question

On 16 June in DR position LAT 50&deg;57.0'S, LONG 53&deg;03.9'W (ZD+4), you take an ex-meridian observation of Acrux at lower transit. The chronometer time of the sight is 10h 08m 18s, and the chronometer error is 02m 12s fast. The sextant altitude (hs) is 23&deg;49.0'. The index error is 1.1' off the arc, and your height of eye is 26 feet. What is the latitude at meridian transit?

Accepted Answer

Option A: 50&deg;41.2'S. Apply the ex-meridian correction to the observed altitude to find the meridian altitude. Use the declination of Acrux and the meridian altitude formula (Lat = 90° - Ho + Dec) to determine the latitude at transit, ensuring all corrections for index error and height of eye are applied.