There is a question in a textbook which states:

"A cyclist is riding north at 12km/s when it starts to rain. The rain appears to be falling towards her at an angle of 10 degrees relative to the vertical. Deciding to return home, the cyclist turns south, riding at the same speed. Now the rain appears to be coming towards her at an angle of 6 degrees to the vertical. What is the velocity of the rain?"

Now, the answers say that the velocity of the rain is 3.5km/h at an angle of 27 degrees to the vertical.

However, I don't see any situation is which this is possible. By travelling north, you're already extending the horizontal velocity of the rain which places it at 10 degrees. By travelling south, you've reduced the velocity of the rain to 0 and then reversed the horizontal velocity so that it now travels at 6 degrees relative to you. Therefore the angle of the rain when you are stationary shouldn't exceed 6 degrees or 10 degrees? I feel as if the interpretation of the question I've used may not be correct.