$16\mathrm{.}55($a$)$ Considering only buckling in the plane of the structure shown and using Euler's formula, determine the value of $$ between $0$ and $90$ for which the allowable magnitude of the load $P$ is maximum. $(b)$ Determine the corresponding maximum value of $P$ knowing that a factor of safety of $3\mathrm{.}2$ is required. Use $E=29{10}^6.$