A cut $8$ m deep i ps to be made in a saturated clay with a unit weight of $18$Kn$/$m$3$ and an undrained cohesion of $27$ kn$/$m$2.$ A hard stratum exists at a depth of $12$ m below the gound surface.

a$)$ determine if a $30$ degrees slope is safe

b$)$ if a factor of safety $1\mathrm{.}50$ is desired, what is a safe angle of slope

c$)$if the angle of residtance is $15$ degrees determine factor of safety

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