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### Discussion :: Height and Distance

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

2.  A. 173 m B. 200 m C. 273 m D. 300 m

Explanation :

Let AB be the lighthouse and C and D be the positions of the ships.

Then, AB = 100 m, ACB = 30° and ADB = 45°.

 $$\frac { AB } { AC }$$= tan 30° = $$\frac { 1 } { 3 }$$         AC = AB x 3 = 1003 m.

 $$\frac { AB } { AD }$$= tan 45° = 1          AD = AB = 100 m.

 CD = (AC + AD) = (1003 + 100) m = 100(3 + 1) = (100 x 2.73) m = 273 m.

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