Question
The angle of elevation of a cliff from a fixed point is ө. After going up a distance of K metres towards the top of the cliff at an angle of φ, it is found that the angle of elevation
is α. Show that the height of the cliff is 
Solution
Let CE be a cliff of height h m. Angle of elevation of cliff from a fixed point A be ө.
i.e., ∠CAE = ө. ∠CAF = φ and AF = k metres. From F draw FD and FB perpendiculars on CE and AC respectively. It is also given that ∠DFE = α.
In right triangle ABF, we have
In right triangle ACE, we have
And, DE = CE - CD = CE - BF
= h - k sin φ.
In right triangle DFE, we have
Hence, the height of the cliff is
