(a) Steps: 1 Mark
     Correct answer: 1 Mark
(b) Formula: 1 Mark
     Result: 1 Mark
(a)

$\angle OAD=50°\left(given\right)\angle DOC=180°-50°=130°\left(linearpair\right)\angle DPC=160°\left(given\right)\angle DPO=180°-160°\left(Linearpair\right)\angle DPO=20°In△DOP\angle ODP=180°-(130°+20°)\left(byanglesumproperty\right)\angle ODP=30°In△DBE\angle DBE=180°-(90°+30°)\left(Byanglesumproperty\right)\angle DBE=60°$
(b)   
     
The wall and the ground are at right angle. Therefore the ladder, ground and the wall make the sides of a right-angled triangle.
$\therefore a^2+{12}^2={15}^2$
$\Rightarrow a^2=225-144=81$
$a=\sqrt{8}1=9m$