Question

a man on a Cliff observe a boat at an angle of depression 30° , which is sailing towards the point of the shore Immediately beneath him. 3 minutes later the angle of depressionof the boat is found to be 60°.assuming that the boat sails at a uniform speed determine how much more than it will take to reach the shore. ​

Answer 1

Step-by-step explanation:

Let height of cliff= AB=h

∠EAD=∠ADB (alternate interior ∠)

=30

o

(Refer to Image)

Also, ∠EAC=∠ACB=60

o

Let speed of boat= V m/s

A/Q, DC=3×60V=180V

Let, BC=x

Time taken from C to B=t

⇒x=vt

Now, in △

le

ABD,tan30

o

=

180v+vt

h

⇒1

3

=

180v+vt

h

In △

le

ABC, tan60

o

=

vt

h

⇒

3

=

vt

h

⇒h=

3

vt

⇒

3

1

=

180v+vt

3

vt

⇒180+t=3t

⇒180=2t⇒t=90s= 1min30sec

solution

Answer 2

The answer is in attached photos.