KCSE 2025 Maths P2 Q8 — Longitude from Distance in Nautical Miles
Published
The Question
“A point U is 9000 nautical miles due east of point T, which lies on the equator at longitude 50 degrees West, written T(0, 50W). Find the longitude at U.”
Note that the whole journey is along the equator
Both T and U lie on the equator, which is itself a great circle. This means the 9000 nautical miles can be measured directly as an arc of the equator, and the distance corresponds straight to a difference in longitude with no latitude adjustment needed.
Along the equator, a change in longitude is measured the same way as a great-circle arc.
Convert nautical miles to minutes, then to degrees
Use the defining rule that one nautical mile equals one minute of arc along a great circle. So 9000 nautical miles is 9000 minutes of arc. Since 60 minutes make one degree, divide by 60 to turn the minutes into degrees of longitude covered.
Travel east from T's longitude
Take east as the positive direction. Point T is at 50 degrees West, which counts as negative 50 degrees. Moving 9000 nautical miles due east adds 150 degrees to this starting longitude. Add the two values to find where you land.
Interpret the sign of the answer
The result is positive 100 degrees. A positive longitude means the point lies east of the Greenwich meridian, so the longitude of U is 100 degrees East.
Final Result
The longitude at U is 100 degrees East. (9000 nautical miles is 150 degrees of longitude; starting at 50 degrees West and moving 150 degrees east gives negative 50 plus 150, which is 100 degrees East.)
Why this method works
The method works because a nautical mile is defined as one minute of arc subtended at the centre of the Earth, so distance along a great circle converts directly into angle. The equator is a great circle, and longitude is measured along it, so 9000 nautical miles is simply 9000 minutes, or 150 degrees, of longitude. Treating east as positive lets you combine the starting longitude and the eastward turn with a single signed addition, and the sign of the total tells you whether the final position is east or west of Greenwich.
West 50 degrees to Greenwich is 50 degrees of arc, then Greenwich to 100 degrees East is another 100 degrees, totalling 150 degrees, which matches the 9000 nautical miles travelled.