Answer
$25.33^o$
Work Step by Step
We call the angle $\vec{F}_1$ makes with the north, which is the direction of the boat's movement, $\theta$
The work done by $F_1$ over $s=52m$ is $W_1=(F_1\cos\theta)\times52$
$F_2$ exerts force on the boat along the same direction as the boat's movement, so the work done by $F_2$ over $s=47m$ is $W_2=F_2\times47$
From the given information, $W_1=W_2$ and $F_1=F_2$, so $$(F\cos\theta)\times52=F\times47$$ $$52\cos\theta=47$$ $$\cos\theta=\frac{47}{52}$$ $$\theta=25.33^o$$
