Problem $\backslash$#$3(20$ points$)$

The effective normal stress on a certain plane at a given point in a soil is $120$ kPa $.$ The effective cohesion and effective friction angle of the soil are $10$ kPa and $\backslash (31^\{\backslash$circ$\}\backslash ),$ respectively. A foundation to be built nearby will induce a shear stress of $50$ kPa on this plane. Using an effective stress analysis, compute the long$-$term factor of safety against shear failure on this plane.