Two ships which are on the same side and at a distance of 40 m apart observes the top of a light house at the angles of elevation 30° and 60°. Find the height of the light house and the distance of the ships from the light house.



Let AB be the lighthouse of height h.Let C and D be the position of the 2 ships, such that CD = 40 m.Let ACB = 60° and ADB = 30°In ABC,     tan 60° = ABBC3 = hBCBC = h3    ....1In ABD,tan 30° = ABBD13 = hBC + CD3h = BC + 403h = h3 + 403h - h3 = 403h - h3 = 402h = 403h = 203Now, from 1, we getBC = 2033 = 20So, height of lighthouse = 203 mDistance of first ship from lighthouse = BC = 20 mDistance of second ship from lighthouse = BD = 20+40 = 60 m

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