$b=6/\cos 14.{04}^o=6.184658438$ = 6185 mm to the nearest mm.

To calculate $a$ first find the angles in the triangle formed by the overhang, the wall of the house and the rays of the sun. These angles in degrees are: $75.96375653,8,96.03624347$ ( $1.325817664,0.13962634,1.67614865$ radians). Using the Sine Rule

${\displaystyle a=\frac{5.5\sin 8}{\sin 96}=0.769719708=770\mathrm{mm}}$

to the nearest mm.