In this problem r is the resultant of p and q, let the angle between r and p is α and r and q is β then 

p = r sin β/sin(α+β)       (1)          and                         q = r sinα/sin(α+β)           (2)

so p/q = sinβ/sinα

and according to given condition p/q = 6/5 so sinβ = 6k and sinα = 5k

now obtain cos function and solve it.