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Please solve the 9 th question.
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Q.9. A man on a cliff observes a boat, at an angle of depression 30 ° , which is sailing towards the shore to the point immediately beneath him. Three minutes later, the angle of depression of the boat is found to be 60 ° . Assuming that the boat sails at a uniform speed, determine :
(i) how much more time it will take to reach the shore ?

Dear Student,


Assuming Man is Standing at point A and observes the boat sailing towards him and moved towards him from C to D changes its angle from 30o to 60o in 3 minutes.and we have to estimate time from to reach to the shore B from D.In △ABCtan 30o=ABBC⇒13=ABBD+CD⇒AB=BD+CD3.................................................................1Now, In △ABDtan 60o=ABBD⇒AB=3 BD.....................................................................2from 1 and 2⇒BD+CD3=3 BD⇒BD+CD=3 BD⇒3BD-BD= CD⇒2 BD= CD⇒BD= CD2.................................................3In Covering CD distance boat had taken 3 minutesSo, In Covering CD2 distance boat will take 32 minutesSo, In Covering BD distance boat will take  1.5 minutes. 
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