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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.
Solution
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.
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