## Trigonometry (11th Edition) Clone

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