Question $1($Rubric $50(1\mathrm{.}1,1\mathrm{.}2),50(1\mathrm{.}3)$

Figure Q$1$ shows a gravity wall and the assumed triangular soil wedge. The soil consists of homogeneous sand with an angle of friction, ${}^{\text{'}}=30$ and a unit weight, $=20k\frac{N}{m^3}.$ The angle of friction between the back of the wall and the soil is $=30.$ All wall dimensions and various angles are shown in the figure.

Calculate the weight of the triangular wedge;

$[5$ marks$]$

$1\mathrm{.}2$ Use Coulomb's theory to draw the polygon of forces indicating all angles;

$[10$ marks$]$

$3$ Calculate the magnitude and direction of the active force on the retaining wall.

$[15$ marks$]$

Figure Q$1$