$1\mathrm{.}24$ At a point in a matcrial, the state of stress in MPa is given by the components ${}_x=12\mathrm{.}8,{}_y=27.{}_z=51\mathrm{.}3,{}_{xy}=23\mathrm{.}4,{}_{zz}=11$ and ${}_{yz}=-6\mathrm{.}24.$ Determine the normal and shear stresses on a plane whose normal makes angles of $48$ and $71$ to the $x$ and $y$ axes respectively. Also find the direction of the shear stress relative to $x$ and $y.$

Answer: $($:$48\mathrm{.}8$MPa,$12\mathrm{.}31$MPa,$137\mathrm{.}8,69\mathrm{.}1,55\mathrm{.}34\}$