What will be the Height of Pole? If

The angle of elevation of sun changes from 30 degree to 45 degree , the length of the shadow of a pole decreases by 4 meters, the height of the pole is
( Assume √3 = 1.732)

  1. 1.464 m
  2.  9. 464 m
  3.  3. 648 m
  4.  5. 464 m

 

Manish Listener Asked on 9th July 2015 in Maths.
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1 Answer(s)

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Answer : (4). 5.464  m

RE: What will be the Height of Pole? If

Let height of pole be ‘h’,

First angle of elevation from sun to pole is 30 degree.
Distance between shadow pole to foot of pole = ‘x’
Therefore, tan30 = h/x
                        1/sqrt (3) = h/x.   
                                         x  = h * 1.732 ……(i)

Second angle of elevation angle from sun to pole is 45 degree,
Distance form foot of pole to shadow of pole = ( x – 4 ).
Therefore, tan45 = h / ( x – 4 ) 
                               1 = h / ( x – 4 )      
                               x  = h + 4             ….(ii)
on comparing eqn. (i) and (ii) we get ,
h * 1.732 = h + 4
                                                                 h (1.732 – 1 ) = 4
                                                                  h  =  4 * 0.732
                                                                  h  =  5.464
Hence, the height of pole is 5.464m

vijay Professor Answered on 13th July 2015.
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