On 7 November your 0830 zone time fix gives you a position of LAT 27°36.0'N, LONG 162°19.0'W. Your vessel is on course 289°T and your speed is 19.0 knots. Local apparent noon (LAN) occurs at 1138 zone time, at which time a meridian altitude of the Sun's lower limb is observed. The observed altitude (Ho) for this sight is 45°35.0'. What is the latitude at 1200 ZT?
• Meridian altitude sight (LAN) and how it gives latitude using Sun’s declination • Converting time between 0830, LAN at 1138, and 1200 to find run at 19.0 knots on course 289°T • Separating north–south (latitude) and east–west (longitude) components of your track between the 0830 fix, LAN, and 1200
• First, think about how a meridian altitude (Sun on your meridian at LAN) relates to your latitude: what basic formula links Ho, Sun’s declination, and latitude? • Before and after LAN, how far does the vessel travel, and how much of that distance is north–south versus east–west on course 289°T? • Is the latitude you compute from the LAN sight at 1138 the final answer, or do you also need to advance that position to 1200 using a run in the direction of your course?
• Compute the run from 0830 to 1138 and from 1138 to 1200 using ( \text{Distance} = \text{Speed} \times \text{Time} ). • Resolve the total run into N–S and E–W components using the course 289°T (use cosine for N–S on a near‑west course). • Use the proper latitude formula for a meridian altitude of the Sun’s lower limb, being careful about the Sun’s declination sign (north or south) on 7 November.
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