Q1 of 12 Page 203

Two ships are there in the sea on either side of a lighthouse in such a way that the ships and the lighthouse are in the same straight line. the angles of depression of two ships as observed from the top of the lighthouse are 60° and 45°. If the height of the lighthouse is 200 m. Find the distance between the two ships

The figure is given below:



Let the distance between the foot of light house (O) to 1st ship(A) be x m


and the distance between lighthouse(O) & 2nd ship(B) be y m.


From figure;


∠ CAO = 60°


∠ CBO = 45°


Using trigonometry;


tan 60° = √3




Also, tan 45° = 1



y = 200


AB = OA + OB



AB = 200 + 115.47 = 315.47 m


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