Question

A man on a cliff observes a boat at an angle of depression 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.​

Answer 1

Answer:

Let the speed be x km/h

Let the time be t

In △ADC,

tan30°= xt/h

1/$\sqrt} 3$= xt/h

h= root 3 xt

in triangle ABD,

tan 60=x(6+t)/root 3

h= x(t+6)/root 3

root 3xt=x(t+6)/2

3t=6+t

t=3 seconds

∴ total time taken=6+3=9 seconds