#### Answer

The magnitude of the resultant force is 280 N
The angle between the resultant force and the first boat's force is $30.3^{\circ}$

#### Work Step by Step

Let $a = 100~N$
Let $b = 200~N$
Let angle $\theta$ be the angle between these two forces. Then $\theta = 45^{\circ}$
We can use the parallelogram rule to find $c$, the magnitude of the resultant force:
$c = \sqrt{a^2+b^2+2ab~cos~\theta}$
$c = \sqrt{(100~N)^2+(200~N)^2+(2)(100~N)(200~N)~cos~45^{\circ}}$
$c = \sqrt{78284.27~N^2}$
$c = 280~N$
The magnitude of the resultant force is 280 N
Let $C = 180^{\circ}-45^{\circ} = 135^{\circ}$
We can use the law of sines to find the angle $B$ between the resultant force and the first boat's force:
$\frac{c}{sin~C} = \frac{b}{sin~B}$
$sin~B = \frac{b~sin~C}{c}$
$B = arcsin(\frac{b~sin~C}{c})$
$B = arcsin(\frac{(200~N)~sin~135^{\circ}}{280~N})$
$B = arcsin(0.505076)$
$B = 30.3^{\circ}$
The angle between the resultant force and the first boat's force is $30.3^{\circ}$