# Determine the magnitude of the resultant force

Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive x axis.

# Solution:

Draw the components as follows. (Note that the diagrams are not to scale)

Draw the vector components tail to tail as follows.

Use cosine law to figure out the resultant force $F_{R}$

$F_{R}=\sqrt{600^2+800^2-(2)(600)(800)(\cos60^0)}$

$F_{R}=721.1N$

Use sine law to figure out angle counter clockwise from the x-axis

$\frac{600}{\sin\theta} = \frac{721.1}{\sin60^0}$

$\theta = 46.1^0$

Subtract $\theta$ from $90^0$ to get the angle between x-axis and the resultant force.

$\phi = 90^0-46.1^0 = 43.9^0$

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