#$1.$ Answer for the following $2$D truss structure.

$(1)$ Obtain reaction forces in $P.$

$(2)$ Compute the internal of each truss member in $P.$ Which truss member has the largest magnitude of the internal force?

$(3)$ The allowable tensile and compressive stresses are $20$MPa and $-20$MPa, respectively. If we decide to use the safety factor of $2$ for $P=500N,a=3m,$ what is the minimum cross section area? Assume all the same cross section areas.