Question

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.

Answer 1

We have
`fa=BC=7m, b=AC=8mand C=AB=9m.`
Let M be the midpoint of AC and let MP be the lamp post of hight h metres.

Then, `/_MBP=theta=tan^(-1)1/3`
Applying cosine formula on `DeltaABC`, we get
`cosC=((a^(2)+b^(2)-c^(2)))/(2ab)=((49+64-81))/(2xx7xx8)=32/112=2/7" ....(i)"`
In `DeltaBMC`, we have
`BC=7m, CM=1/2CA=4m.`
`=(49+16-2xx7xx4xx2/7)=49" [Using (i)]"`
`rArr" "BM=7m.`
From right `DeltaBMP`, we have
`tantheta=(PM)/(BM)=h/7rArrh/7=tan(tan^(11)3)=3rArrh=21m.`
Hence, the heith of the lamp post is 21 m.