# #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 $$r$$.

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