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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 Topperlearning User 27th July 2017, 11:02 AM
Answered by Expert
Answer:

Let A and D be the positions of the boat at the two instants.

Let the speed of the boat be v m/min.

Therefore, AD= 6v metres

Let the boat takes t minutes to reach from D to B.

Thus, BD= vt metres

In DBC,

= tan60o

=

h= vt ….(i)

In ABC,

= tan30o

=

h= ….(ii)

From (i) and (ii),

vt =

3vt = 6v+vt

2vt=6v

t = 3

Thus, the time taken to reach the shore is 3 minutes.

Answered by Expert 27th July 2017, 1:02 PM
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