Raising the Roof
Slope of roof (pitch) = $\tan^{-1}(1.5/6)= 0.244978663$ radians =
14.03624347 degrees.
$b= 6/\cos 14.04^o = 6.184658438$ = 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
$$a= {5.5 \sin 8\over \sin 96} = 0.769719708 = 770 {\rm mm}$$ to
the nearest mm.