Two ships are there in the sea on either side of a light house in such a way that the ships and the light house are in the same straight line. the angles of depression of two ships as observed from the top of the light house are 60 degree and 45 degree. if the height of the light house is 200 m , find the distance between the two ships.




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Let the ships be at A and B and the top of the light house be C as shown in the figure.
The distance between the ships id AB
given that OC = 200m

tan45 = OC/OB
⇒ 1 = 200/OB
⇒OB = 200m

tan 60 = OC/AO
⇒√3 = 200/AO
⇒AO = 200/√3 = 115.47m

AB = AO+OB = 200+115.47 = 315.47m
Distance between ships is 315.47m

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Let P and Q be the two ships and AB be the light house tan45 =AB/BP 1=200/BP BP=200 tan60=AB/BQ 1.732=200/ BQ BQ=200/1.732 BQ=115.7 PQ=PB+BQ PQ=200+115.7 PQ=315.7