A lamp post is situated at the middle point M of the side AC of a triangular plot of ABC with `B C=7m ,\ C A=8\ a n d\ A B=9mdot` Lamp post subtends an angle of `15^0` at the point B. determine the height of the lamp post.

Explanation

Here, a=BC=7 m
b=CA=8m
c=AB=9m
Let MP=hm = height of lamp post
`cosC=(a^(2)+b^(2)-c^(2))/(2ab)`
`=(7^(2)+8^(2)-9^(2))/(2 xx 7 xx 8)`
`=2/7`
Given that `anglePBM=15^(@)`
In `DeltaBMC`
`cosC=(BC^(2)+CM^(2)-BM^(2))/(2.BC.CM)`
`rArr 2 xx 7 xx 4 xx 2/7 = 7^(2)+4^(2)-BM^(2)`
`rArr BM^(2)=7^(2)`
`rArr` BM=7m
In `DeltaBMP=90^(@)`
`tantheta=(PM)/(BM)`
`rArr PM=BMtantheta`
`rArr h=7.tan15^(@)`
`=7(2-sqrt(3))` m.