The angle of elevation of a cliff from a fixed point A is θ. After going up adistance of k metres towards the top of the cliff at an angle φ, itis found that the angle of elevation is α. Show that the height ofthe cliff in metre is 
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Given:
Angle of elevation from fixed point A = θ
Distance covered = k m
Angle after the distance k metres is covered = ϕ
In right angled Δ FED,
FE = k m
sin φ = ED / FE
∴ ED = FE sin φ
= k sin φ
Again, cos φ = FD / FE
∴ FD = FE cos φ
= k cos f .....................(1)
In right angled Δ AFC,
FC / AC = cot θ
FC = AC cot q................................... (2)
FC - FD = DC
But, DC = EB
∴ EB = FC – FD
Thus, EB = AC cot θ - k cos f …………………. (from (1) and (2))
Now, AB = AC - BC
But, BC = ED = k sin φ
∴ AB = AC - k sin φ
In right angled Δ AEB, cot α = EB / AB
AC cot θ - k cos φ = AC cot α - k sin φ cot α
AC cot θ - AC cosα = k cos φ - k sin φ cot α
AC (cot θ - cot α ) = k cos φ - k sin φ cotα
Hence proved the height of the cliff in metres is 