Question

34.
The angle of elevation of the top of a cliff from a fixed point is 0. After going up a distance k
meters towards the top of the cliff at an angle Ø, it is found that the angle of elevation is a, show
k(cos 0-sin cota)/
coto-cot a​

Answer 1

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cotθ−cotαk(cosϕ−sinϕcotα)

Hard

Answer

The pictorial representation of the given data is represented by the figure

In ΔDEF,DFDE=sinϕ,DFEF=cosϕ

 

⇒DE=ksinϕ,EF=kcosϕ  [DF=kkm]

 

Let AB=x

 

∴AC=AB−BC=AB−DE=x−ksinϕ

 

In ΔACD,CDAC=tanα

 

⇒CDx−ksinϕ=tanα

 

⇒CD=(x−ksinϕ)cotα

 

BF=EF+BE=EF+CD=kcosϕ+(x−ksinϕ)cotα

 

In ΔABF,BFAB=tanθ

 

⇒kcosϕ+(x−ksinϕ)cotαx=tanθ

 

⇒xcotθ=kcosϕ+xcotα−ksinϕcotα

 

⇒(cotθ−cotα)x=k(cosϕ−sinϕcotα)

 

⇒x=cotθ−cotαk(cosϕ−sinϕcotα)

 

Thus the height of the cliff is cotθ−cotαk(cosϕ−sinϕcotα)