Question

Two men on either side of a cliff 75 m high observe the angles of elevation of the top of the cliff to be 30° and 60°. Find the distance between the two men.

Answer 1

In ΔBAD,

tan 60° = `("AB")/("AD")`

⇒ `sqrt(3) = 75/("AD")`

⇒ AD = `75/sqrt(3) xx sqrt(3)/sqrt(3)`

= `(75sqrt(3))/3`

= `25sqrt(3)` m  ...(i)

and In ΔBAC,

tan 30° = `("AB")/("AC")`

⇒ `1/sqrt(3) = 75/("AC")`

⇒ AC = `75sqrt(3)` m  ...(ii)

From equations (i) and (ii), we have

DC = AC + AD

= `75sqrt(3) + 25sqrt(3)`

= `100sqrt(3)`

= 100 × 1.732

= 173.2 m

Which is the required distance between two men.