P$4\mathrm{.}4$ A vector polygon for summing $2$ kN and $7$ kN forces is shown $($Figure P$4\mathrm{.}4).$ Determine

Figure P$4\mathrm{.}4$

Details

A vector diagram shows a vector of magnitude $2$ kilonewtons acting downward from the start point, and another vector of magnitude $7$ kilonewtons acting upward to the left toward the end point. The second vector is at an angle of $55$ degrees relative to the horizontal. The resultant vector $\backslash ($ R $\backslash )$ extends upward to the left, from the start point to the end point, at an angle of theta relative to the horizontal.

$($a$)$ the magnitude $\backslash ($ R $\backslash )$ of the resultant by using the law of cosines and

$($b$)$ its angle of action $\backslash (\backslash$theta $\backslash )$ by using the law of sines.