# #2015_4 Height of a street lamp?

**Geometry**Level 4

A lamp post is situated at the middle point \(M\) of the side \(AC\) of a triangular plot \(ABC\) with \(BC=7 \text { m}\), \(CA=8 \text { m}\) and \(AB=9 \text { m}\). Lamp post subtends an angle \(15^\circ\) at the point \(B\). The height of the lamp post is of the form \(p(q-\sqrt { r } ) \text{ m} \), then find the sum of \(p, q \) and \(r\).