A force of magnitude $F{\text{ }}N$ acts in a horizontal plane and has components $27.5{\text{ }}N$ and $ - 24{\text{ }}N$ in the x-direction and the y-direction respectively. The force acts at an angle of ${\alpha ^ \circ }$ below the x-axis.
a) Find the values of $F$ and $\alpha $.
A second force, of magnitude $87.6{\text{ }}N$, acts in the same plane at ${90^ \circ }$ anticlockwise from the force of magnitude $F{\text{ }}N$. The resultant of the two forces has magnitude $R{\text{ }}N$ and makes an angle of ${\theta ^ \circ }$ with the positive x-axis.
b) Find the values of $R$ and $\theta $.
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