# Question #5de41

Jun 21, 2015

The answer is $\sqrt{37} \text{N}$.

#### Explanation:

Because the angle between the two forces is not ${90}^{\circ}$, you cannot apply Pythagoras' Theorem to determine the magnitue of the resultant.

However, you can apply the Parallelogram of force to determine the magnitude of the resultant.

The formula you're going to use looks like this

${F}^{2} = {F}_{1}^{2} + {F}_{2}^{2} + 2 {F}_{1} {F}_{2} \cos \left(\theta\right)$, where

$\theta$ - the angle between the two forces, in your case equal to ${120}^{\circ}$.

This means that you have

${F}^{2} = {4}^{2} + {7}^{2} + \cancel{2} \cdot 4 \cdot 7 \cdot \left(- \frac{1}{\cancel{2}}\right)$

${F}^{2} = 16 + 49 - 28 = 37 \implies F = \textcolor{g r e e n}{\sqrt{37} \text{N}}$