The angle of elevation of the top of a pillar of height h at a point on the ground at a distance x from the pillar is `30^(@)`. On walking a distance 'd' towards the pillar the angle of elevation becomes `60^(@)`. Then, which one of the following is correct?

Options

A. x=d+h
B. `x=(3d)/(2)`
C. `x=(5d)/(4)`
D. `x=2d`

Answer

B

Explanation

Let DC be the pillar of height h and A be the point at a distance x from pillar such that `angle CAD = 30^(@)`. On walking a distance d towards pillar (point B) `angle CBD= 60^(@)`. So, in `Delta BCD`,
`tan 60^(@)=(CD)/(BC)`
`rArr sqrt(3)=(h)/(x-d)`
`rArr h=sqrt(3) (x-d) " " ...(i)`

and in `Delta ACD`,
`tan 30^(@) = (CD)/(AC)`
`rArr (1)/(sqrt(3))=(h)/(x)`
`rArr x=hsqrt(3)`
`rArr =3 (x-d)` (using Eq. (i))
`rArr x=3x-3d`
`rArr 2x=3d`
`rArr x=(3d)/(2)`