What will be the Distance of the Object? If

From the top of a tower of height 180 m the angles of depression of two objects on either sides of the tower are 300 and 450 . Then the distance between the objects are

  1. 180 (3+√3) m
  2. 180 (3-√3) m
  3. 180 (√3-1) m
  4. 180 (√3+1) m
Manish Listener Asked on 18th July 2015 in Maths.
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    Answer:  (3) 180 (√3-1) m
    Explanation:-
    According to the question,
    In the figure-

    RE: What will be the Distance of the Object? If


    The height of the tower is BC = 180 m  and  A & D are two objects which given in the question.
    In right angle right triangle BCD,
    tan45o = 180/BD
    1 = 180/BD
    Then, BD = 180 m                      ……………………… (1)
    Now, In right triangle ABC,
    tan30o = 180/(AD + BD)
    1/√3 = 180/(AD + 180 )                          {from equation (1) }
    AD + 180  = √3 x 180                            ( by cross multiplication)
    AD =  180√3 – 180
    AD = 180(√3- 1)
    AD = distance between two objects.
    Hence, the answer is (3) 180 (√3 – 1) m.

    Anurag Mishra Professor Answered on 18th July 2015.
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