a man on  a  cliff observes a boat at an angle of depression of 30 which is approaching the shore to the point immediately beneath the observer with a uniform speed . six minutes later , the angle of depression of the boat is found to be 60 . find the time taken by the boat to reach the shore .

Asked by Sanchit Sharma | 13th Mar, 2015, 06:16: PM

Expert Answer:

Hi Sanchit,

 

tan 30 to the power of degree equals fraction numerator x over denominator A B end fraction fraction numerator 1 over denominator square root of 3 end fraction equals fraction numerator x over denominator A B end fraction A B equals square root of 3 x space.... left parenthesis 1 right parenthesis  tan 60 to the power of degree equals fraction numerator x plus y over denominator A B end fraction square root of 3 equals fraction numerator x plus y over denominator A B end fraction square root of 3 A B equals x plus y..... left parenthesis 2 right parenthesis  p u t space left parenthesis 1 right parenthesis space i n space left parenthesis 2 right parenthesis square root of 3 square root of 3 x equals x plus y 3 x equals x plus y 2 x equals y..... left parenthesis 3 right parenthesis  B o a t space t a k e s space 6 space m i n u t e s space t o space t r a v e l space t h e space d i s tan c e space y space u n i t s.  A s space space t h e space s p e e d space i s space s a m e comma space s o space t h e space t i m e space t a k e n space b y space b o a t space t o space t r a v e l space x space u n i t s space i s space h a l f space o f space t h e space t i m e space t a k e n space t o space t r a v e l space y space u n i t s. space left parenthesis f r o m space 3 right parenthesis  S o space t h e space t i m e space t a k e n space b y space b o a t space t o space t r a v e l space x space u n i t s space i s space 3 space m i n u t e s.  S o space t o t a l space t i m e space t a k e n space b y space b o a t space equals space 3 plus 6 space equals 9 space m i n u t e s

 

 

 

Answered by  | 13th Mar, 2015, 06:42: PM

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