Question

The angle of elevation of a cliff from a fixed point is θ. 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 a. Show that the height of the cliff is k(cosϕ-sinϕ cot α)/(cotϕ-cotα) metres.     

Answer 1

Let AB be the cliff and O be the fixed point such that ∠AOB =θ. Let ∆AOC =ϕ  and OC = km. From C, draw CD and CE perpendiculars on AB and OA, respectively. Now, ∠DCB = a. Let h be the height of the cliff AB. In ∆COE, we have