finding the magnitude using vector

Hi

I need help on the following question:

The direction of force F1 is in a direction west of north with magnitude of 5 newton, and force F2 is unchanged ( which is northeast with a magnitude of 6 newton). If the resultant force F = F1 + F2 now points directly to the north, find the direction of F1 and the resulting F.

My problem is i cannot seem to get the magnitude but i can get the direction:

This is how i got the direction:

When i drew the vectors it was not a right angle triangle so i used this formula:

degrees

This is my attempt of finding the magnitude:

using the formula:

F = 5.41N however book's answer says its 6.89N

P.S