$6.$ From one corner of a triangular plot of land, a surveyor determines the directions to the two other corners to be $\backslash (\backslash$mathrm$\{$N$\}32^\{\backslash$circ$\}\backslash$mathrm$\{$E$\}\backslash )$ to point A and $\backslash (\backslash$mathrm$\{$S$\}76^\{\backslash$circ$\}\backslash$mathrm$\{$E$\}\backslash )$ to point B $.$ What is the measure of the angle formed by the edges of the plot of land at the corner where the surveyor is standing? If the distance from the surveyor to point A is $150$ ft and the distance from the surveyor to point B $210$ ft $,$ how far apart are point $\backslash ($ A $\backslash )$ and $\backslash ($ B $\backslash )$ and what is the area of the plot of land?