Question

please solve this problem fast and show step by step​

Answer 1

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,  AC/CD =tanα

⇒x−ksinϕ  /CD  =tanα

⇒CD=(x−ksinϕ)cotα

BF=EF+BE=EF+CD=kcosϕ+(x−ksinϕ)cotα ​  

In ΔABF, AB/ BF =tanθ

⇒  x/kcosϕ+(x−ksinϕ)cotα  =tanθ

⇒xcotθ=kcosϕ+xcotα−ksinϕcotα

⇒(cotθ−cotα)x=k(cosϕ−sinϕcotα)

⇒x=k(cosϕ−sinϕcotα)/cotθ−cotα

where x = height of the cliff

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