Find the length of pq. round to the nearest hundredth.

Angle R is the reference angle as its the only given angle (other than the 90 degree angle). 

Opposite angle R is segment PQ
PR is the hypotenuse

Use the sine rule to find that...
sin(angle) = opposite/hypotenuse
sin(R) = PQ/PR
sin(19) = PQ/11
11*sin(19) = PQ
PQ = 11*sin(19)
PQ = 3.58124969902872 <<-- use a calculator (degree mode)
PQ = 3.58

3.58