Determine the magnitude of the resultant force acting on the screw eye and its direction measured clockwise from the x axis.

Solution:

Draw the components as follows.

(Remember to use the angle theorems with parallel lines)

Draw the vector components tail to tail as follows.

Use cosine law to figure out $F_{R}$

F_{R} =\sqrt{6000^{2}+2000^{2}-(2)(6000)(2000)(\cos(105^{0}))}

F_{R} =6798N

Use sine law to figure out $\theta$

\frac{6798N}{\sin105^0}=\frac{6000N}{\sin\theta}

\theta = 58.5^0

To find the angle clockwise from the x-axis, add $58.5^0 + 45^0 = 103.5^0$

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