Let Vc is velocity of cyclist and Vr is velocity of falling rain
Now, woman must hold her umbrella in the direction of the relative velocity (V) of the rain wrt woman.
V = Vr + (-Vc)
V = 30 + (-10) = 20 m/s
tan Ɵ = Vc/Vr = 10/30
Ɵ = tan^-1 (1/3)
Ɵ = 18ᵒ
Thus, woman must hold the umbrella toward the south, at an angle of nearly 18ᵒ with the vertical.