Hello!
The answer is:
According to the picture, the angle that the boat should head upstream is 19° north of west.
Why?
From the figure, we can see that there is a right triangle formed, and since we know its hypothenuse and its opposite side, we can use the following trigonometric relation:
[tex]Sin(\alpha)=\frac{opposite}{hypothenuse}[/tex]
We are given that:
[tex]opposite=6\\hypothenuse=18[/tex]
So, substituting and calculating, we have:
[tex]Sin(\alpha)=\frac{6}{18}[/tex]
[tex]Arcosin(Sin(\alpha))=Arcsin(\frac{6}{18})\\\\\alpha =19.47\°[/tex]
Therefore the angle that the boat should head upstream is 19°, but since speeds and direction and involved, we need to look for the direction, we can see that the vertical speed is due to north, and the horizontal speed is due to west, knowing that, we can conclude that the resultant speed will be due to north of west.
Hence,  according to the picture, the angle that the boat should head upstream is 19° north of west.
Have a nice day!
