Question

Two men on either side of the cliff 80 m high observes the angles of elevation of the top of the cliff to be 30° and 60° respectively. Find the distance between the two men.

Answer 1

In fig. AB be the height of the cliff. 

Let the distance between the two men is DC. 

DC = (x + y) m. 

In ∆ABC 

tan 60° = \(\frac{AB}{BC}\)

√3 = \(\frac{80}{y}\)

√3 y = 80

y = \(\frac{80}{\sqrt3}\)

y = \(\frac{80\sqrt3}{3}\)......(1)

In ∆ABD

Therefore distance between two men is 184.75 m.