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

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By: guest on 01 Jun 2017 05.46 pm

Let AB be the lighthouse and C and D be the positions of the ships. Then, AB = 100 m, ACB = 30° and ADB = 45°. AB = tan 30° = 1 AC = AB x 3 = 1003 m. AC 3 AB = tan 45° = 1 AD = AB = 100 m. AD CD = (AC + AD) = (1003 + 100) m = 100(3 + 1) = (100 x 2.73) m = 273 m.