When the boat is anchored in the harbour, the flag flutters along the N-E direction. It shows that the velocity of wind is along the north-east direction. When the boat starts moving, the flag will flutter along the direction of relative velocity of wind w.r.t. boat. Let $\vec{v}_{wb}$ be the relative velocity of wind w.r.t. boat and β be the angle between $\vec{v}_{wb}$ and $\vec{v}_{w}$. Refer Fig.Now, $\vec{v}_{wb}=\vec{v}_w+(-\vec{v}_b)$Here, $|\vec{v}_w|=72\,\text{km/h}$$|-\vec{v}_b|=51\,\text{km/h}$Angle between $\vec{v}_w$ and $-\vec{v}_b$ is $135^{\circ}$ i.e. $\theta=135^{\circ}.$Then$\tan\beta=\frac{51\sin135^{\circ}}{72+51\cos135^{\circ}}$ $=\frac{51\sin45^{\circ}}{72+51(-\cos45^{\circ})}$$=\frac{51\times\frac{1}{\sqrt{2}}}{72-51\left(\frac{1}{\sqrt{2}}\right)}=1.0039$$\therefore\beta=\tan^{-1}(1.0039)=45.1^{\circ}$Angle w.r.t. east direction $=45.1^{\circ}-45^{\circ}=0.1^{\circ}$It means the flag will flutter almost due east.