Q10
Drop a perpendicular from C to PB; let the foot of this perpendicular be R
Now use this simple fact: if you have a right-angled triangle, hypotenuse of length 'h', with one angle @.
Then the 2 sides: one opp the angle @ and the other adjacent have lengths immediately:
h sin@ and h cos@ respectively.
Now angle CBR = angle PAB = @
Using this fact: AP = x cos @ and PQ = CR = y sin@
.: AQ = AP + PQ = x cos@ + y sin@