Question

an observer on top of a ciff,200m above the sea level,observes the angle of depression of the 2 ships to be 45 degree and 30 degree respectively.find the distance between the ships,if the ships are_ on the same side of the cliff and on the opposite side of the ciff

Answer 1

Given:

Height of the cliff  AB = 200m

Angle of depression of ships = 45° and 30°

To Find:

Distance between the ships, if:

1. the ships are on the same side of the cliff.
2. the ships are on the opposite sides of the cliff.

Solution:

1.  Ships are on the same side

 Distance between the ships is given by:

     $BC= AB cot 45$

     $BD= ABcot30$

     $CD= BD-BC$

     $CD= AB( cot 30-cot45)$

            = $200(\sqrt{3} -1)$

2. Ships on the opposite sides

       Distance between the ships is given by:

        $BC = AB(cot45)$

        $BD=AB(cot30)$

        $CD=BC+BD$

               =$AB(cot45+cot30)$

               =$200(\sqrt{3} +1)$