Finding latitude and longitude

Question

Suppose that P is the north pole and points X and Y in the northern hemisphere are 45◦ apart and form a triangle P XY with angles 60◦ at X and 80◦ at P. Find the latitude of Y . Can you determine the longitude of Y ?

So, I need to find the side PY and for that I use the law of sins:

$$\frac{\sin(80◦)}{\sin (45◦)}=\frac{\sin(60◦)}{\sin (PY◦)}$$

and i got PY=38.4

so to find latitude, I just did: 90◦-38.4◦=51.55◦ N.

The question is how can I find longitude or can I?I don't see any given information besides the north pole coordinates, otherwise if anyone can advise me that would be great!

Answer 1

Suppose you found exact coordinates (latitude and longitude) of two points $X$ and $Y$ that (together with the north pole) made a triangle with exactly the properties described in the question. Now move both $X$ and $Y$ one degree east. Are there any conditions in the question that the new triangle fails to satisfy?

Answer 2

You do not know where or how near the greenwich/prime merdian you are located. Therefore, longitude cannot be found. Otherwise, your latitude looks correct.