A man on a top of a tower observes a truck at an angle of depression α where tanα = 1/√5 and sees that it is moving  towards the base of the tower. Ten minutes later, the angle of depression of the truck is found to be β where tan β=√5, if the truck is moving at a uniform speed, determine how much more time it will take to reach the base of the tower...

10 minutes=600sec

Ans:    Let the speed of the truck be x m/sec  CD=BC-BD

In  right triangle ABC

tanα = h/BC  tanα = 1/√5

BC=h√5............. 1

In right triangle ABD

tanβ= h/BD

h=√5BD                                     ( tan β=√5 )

CD=BC-BD ( CD=600x )

600x =5BD-BD BD=150x

Time taken = 150x /x

=150 seconds

Time taken by the truck to reach the tower is 150 sec.