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.

In fig. AB be the height of the cliff.

Let the distance between the two men is DC.

DC = m.

In ∆ABC

tan 60° =

√3 =

√3 = 80

------(1)

In ∆ABD

tan 30° =

--------(2)

Adding eqn. (1) and (2) we get,

=

⇒ ⇒ ⇒ 184.75 m.

Therefore distance between two men is 184.75 m.