A straight highway leads to the foot of a tower .A man standing at the top of the tower

Observes a car at angle of depression of 30 , which is approaching to the foot of the tower with a

uniform speed . 6 second later the angle of depression of the car is found to be 60 . find the further

time taken by the car to reach the foot of the tower .

let the speed be x

time taken from 30 degree to 60 degree=6sec

time taken from 60 degree to the foot of the tower =tx

In triangle ABD

tan 30=AB/DB

1/ROOT 3=AB/DB

DB=AB root3   =>6x+tx/root 3=AB                  .......(1)

In triangle ABC

tan 60 degree=AB/BC

root 3 tx=AB                                                        ..........(2)

from (1) & (2)

6x+tx/root 3=root 3 tx

6x=2tx

6=2t

therefore t=3