The angle of elevation of a cliff from a fixed point is `theta`. After going up a distance of `k` meters towards the the top the cliff at an angle of `phi`, it is found that the angle of elevation is `alpha`. Show that the height of cliff is ` k(cos phi - sin phi cot alpha)/(cot theta - cot alpha)`

Explanation

{In}` Delta {DEF}`,` frac{{DE}}{{DF}}=sin phi, frac{{EF}}{{DF}}=cos phi`

`=D E=k sin phi, E F=k cos phi[D F=k {km}]`

Let A B=x

A C=A B-B C=A B-D E`=x-k sin phi`

{In} A {ACD},` frac{{AC}}{{CD}}=tan alpha`

`=frac{x-3 sin phi}{C D}=tan alpha`

`=C D=(x-k sin 0) cot alpha`

B F=B F+B E=E F+C D`=k cos phi+(x-k sin 0) cot alpha`

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