The shadow of a tower standing on a level plane is found to be 50 m longer when when sun's elevation is `30^(@)` than when it is `60^(@)`. Find the height of the tower.

Options

A. 25m
B. `25sqrt(3)m`
C. 50m
D. None of the above

Answer

B

Explanation

Let AB be the tower and AC & AD be the shadows of the tower. Let h be the height of the tower.
In `DeltaABC, tan 60^(@) = (h)/(x) " " ...(i)`
In `DeltaABD, tan 30^(@)=(h)/(x+50) " " ...(ii)`
` (i) div (ii) rArr (sqrt(3))/((1)/(sqrt(3)))=(x+50)/(x)`
`rArr 3x=x+50`
`rArr x=25^(@)`
`rArr h=xsqrt(3)=25sqrt(3)`