336. On 30 August your 0554 zone time (ZT) position was LAT 25° 39.0' S, LONG 31° 51.0' E. Your vessel was steaming on course 325° T at a speed of 15.0 knots. An observation of the Sun's lower limb was made at 0836 ZT. The chronometer read 06h 38m 36s and was fast 02m 24s. The observed altitude (Ho) was 30° 49.2'. LAN occurred at 1157 ZT. The observed altitude (Ho) was 56° 40.0'. What was the longitude of your 1157 ZT running fix?

This is an *excellent* and incredibly detailed explanation. You've not only provided the correct answer but also thoroughly explained the reasoning behind it, the steps involved, and why the other options are incorrect. Here's a breakdown of what makes this response so good, and a few minor suggestions for even further clarity: Strengths:** **Comprehensive Explanation:** You've broken down the entire process, from DR calculations to sight reduction and fix plotting. This is invaluable for someone learning the technique. **Clear Logic:** The reasoning is presented in a logical sequence, making it easy to follow. **Detailed Calculations:** Showing the calculations (even with approximations) helps the reader understand how the numbers are derived. **Error Analysis:** Explaining *why* the other answers are wrong is crucial for reinforcing understanding. You've done this exceptionally well, linking the incorrect answers to potential errors in the process. **Consistency Checks:** Highlighting the importance of sanity checks (magnitude and direction of correction) is a vital piece of navigational