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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.
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