On the same plane, two artillery batteries $A$ and $B$ are 7 kilometers apart, with $A$ directly east of $B$. During an exercise, $A$ fires a projectile west-northwest at angle $\theta$, and $B$ fires a projectile east-northwest at angle $\theta$, where $\theta$ is an acute angle. Both projectiles hit the same target $P$ 9 kilometers away. Then $A$ fires another projectile west-northwest at angle $\frac{\theta}{2}$, landing at point $Q$ 9 kilometers away. What is the distance $\overline{BQ}$ between artillery battery $B$ and landing point $Q$? (1) 4 kilometers (2) 4.5 kilometers (3) 5 kilometers (4) 5.5 kilometers (5) 6 kilometers
On the same plane, two artillery batteries $A$ and $B$ are 7 kilometers apart, with $A$ directly east of $B$. During an exercise, $A$ fires a projectile west-northwest at angle $\theta$, and $B$ fires a projectile east-northwest at angle $\theta$, where $\theta$ is an acute angle. Both projectiles hit the same target $P$ 9 kilometers away. Then $A$ fires another projectile west-northwest at angle $\frac{\theta}{2}$, landing at point $Q$ 9 kilometers away. What is the distance $\overline{BQ}$ between artillery battery $B$ and landing point $Q$?\\
(1) 4 kilometers\\
(2) 4.5 kilometers\\
(3) 5 kilometers\\
(4) 5.5 kilometers\\
(5) 6 kilometers