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Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30コ

and 45コ respectively. If the lighthouse is 100 m high, the distance between the two ships is:



Let AB represent the lighthouse and C & D represent the position of ships Then AB is given equal to 100 m and angle ADB=45 degree and angle ACB= 30 degree

tan30 = 1/√3 = AB/AC ⇒AC = AB*√3 = 100√3 m

tan45 = 1 = AB/AD  ⇒ AD=AB = 100 m

Hence distance between two ships,CD = AC+AD = (100√3+100) m

                                                                        =100(√3+1) m

                                                                         =(100*2.73) m = 273 m    

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