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:

$\displaystyle \frac{sinA}{a} = \frac{sinB}{b}$

$\displaystyle sin\theta = \frac{6sin(45)}{5}$

$\displaystyle \theta = 58.05$degrees

This is my attempt of finding the magnitude:

using the formula: $\displaystyle c^2 = a^2 + b^2 - 2abcos(\theta)$

$\displaystyle F^2 = 5^2 + 6^2 - 2 * 5 * 6 * cos(58.05)$

$\displaystyle F = \sqrt{61 - 60cos(58.05)}$

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

P.S