Question

the angle of elevation of cliff from a fixed point is theta .After going up a distance of k metres towards the top of the cliff at an angle of a,it is found that the angle of elevation is alpha.show that the height iof cliff is ,
k(cosa- sina×cotalpha)/cot theta- cotalpha

Answer 1

$\textbf{Answer is in Attachment !}$

Answer 2

Answer:

Step-by-step explanation:

In ΔDEF,

DF

DE

​

=sinϕ,

DF

EF

​

=cosϕ

⇒DE=ksinϕ,EF=kcosϕ  [DF=kkm]

Let AB=x

∴AC=AB−BC=AB−DE=x−ksinϕ

In ΔACD,

CD

AC

​

=tanα

⇒

CD

x−ksinϕ

​

=tanα

⇒CD=(x−ksinϕ)cotα

BF=EF+BE=EF+CD=kcosϕ+(x−ksinϕ)cotα

In ΔABF,

BF

AB

​

=tanθ

⇒

kcosϕ+(x−ksinϕ)cotα

x

​

=tanθ

⇒xcotθ=kcosϕ+xcotα−ksinϕcotα

⇒(cotθ−cotα)x=k(cosϕ−sinϕcotα)

⇒x=

cotθ−cotα

k(cosϕ−sinϕcotα)

​