MathematicsA 1.6 m   tall girl stands at a distance of 3.2 m   from a lamp post and casts a shadow 4.8 m   on the ground. Find the height of the lamp post.

A 1.6 m   tall girl stands at a distance of 3.2 m   from a lamp post and casts a shadow 4.8 m   on the ground. Find the height of the lamp post.


  1. A
    2.67m  
  2. B
    2.57m  
  3. C
    3.67m  
  4. D
    3.57m   

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    Solution:

    It is given that the height of the girl is 1.6m, distance between the lamp post and the girl is 3.2 m and distance between the shadow and the girl is 4.8 m.
    ⇒tanθ= Perpendicular Base    In the triangle CQP,
    ⇒tanθ= PQ QC  
    ⇒tanθ= 1.6 4.8  
    ⇒tanθ= 1 3 ....... 1  
    In the triangle ACP,
    ⇒tanθ= AB BC  
    ⇒tanθ= AB 3.2+4.8  
    ⇒tanθ= AB 8 ........ 2  
    Now, equate the equations (1) and (2) to determine the height of the lamp post,
    ⇒ 1 3 = AB 8  
    ⇒AB= 8 3  
    ⇒AB=2.67m  
    Hence, the height of the lamp post is 2.67m.
    Therefore, the correct answer is option (1).
     
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