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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

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    Answer : Option C

    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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