The horizontal distance between two stations P and Q is $100 \: m$. The vertical angles from P and Q to the top of a vertical tower at $T$ are $3^{\circ}$ and $5^{\circ}$ above horizontal, respectively. The vertical angles from P and Q to the base of the tower are $0.1^{\circ}$ and $0.5^{\circ}$ below horizontal, respectively. Stations P, Q and the tower are in the same vertical plane with P and Q being on the same side of $T$. Neglecting earthâ€™s curvature and atmospheric refraction, the height (in m) of the tower is

- $6.972$
- $12.387$
- $12.540$
- $128.745$