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A man standing in the balcony of a multi-storeyed observes a car at an angle of depression `alpha`where `tan alpha =1/sqrt(5)`. This car is moving towards the base of the building.Ten minutes later the angle of depression of the car is found to be `beta` where `tan beta=sqrt(5)`. If the car is moving at a uniform speed, determine how much more time will it take to reach the base of the building.

Text Solution

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`tanbeta=h/a`
`sqrt5=h/a`
`h=sqrt5a`
`tanalpha=h/a+b`
`1/sqrt5=h/(a+b)`
`(a+b)=sqrt5h`
`a+b=sqrt5xxsqrt5xxa=5a`
`b=5a-a=4a`
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