Question

Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point P between them on the road, the angle of elevation of the top of one pole is `60^(@)` and the angle of depression from the top of another pole and distances of the point P from the poles.

Answer 1

Correct Answer - `20sqrt(3) m ; 20 m` from left pole and `60 m` from right pole
From height `DeltaPAB`, we have
`(AB)/(AC) = tan 60^(@) = sqrt(3)`
`rAr h = x sqrt(3)"……." (i)`
From right `DeltaPCD`, we have
`(CD)/(PC) = tan30^(@) = 1/(sqrt(3))`.
`rArr h = ((80-x))/(sqrt(3))"……."(ii)`

`:. xsqrt(3) = ((80-x))/(sqrt(3)) rArr 3x+x = 80`
`rArr 4x = 80 rArr x = 20`
`:.` height `= 20sqrt(3)m`.
P is 20m from left pole and 60 m from right pole.