From the foot of a hill the angle of elevation of the top of a tower is found to be 45o . After walking 2 km upwards along the slope of the hill which is inclined at30o , the same is found to be 60o . Find the height of the tower.

Answer :

Let ,
We have height of the tower = h


From the image =

tan 45°h + h'b1 + b2

1 = h + h'b1 + b2                                           ( As we know tan 45° =  1 )

h  + h '  =  b1 + b2                                                      ------------------ ( 1 )

And 

cos 30°  = b12

32 = b12                                                                           ( As we know cos30°  = 32 )

b1 = 3                                                     ------------------ ( 2 )
 
And
sin 30°  = h'2

12  =h'2                                                                                                     ( As we know sin 30°  =  12  )

SO,

h'  = 1                                                    ------------------ ( 3 )

And 
tan 60°  = hb2

3    = hb2

h  =  3  b2                                                     ------------------ ( 4 )

 

from equation 1 , 2 , 3  and 4 , we get

h  = 3  + h3 -  1

 h3= 3  -  1

3h - h3 = 3  -  1

3 h - h  =  3 - 3 

3 h - h  =  3 ( 3 - 1 ) 

h ( 3  -  1 ) = 3  ( 3  - 1 )

h  =  3    = 1.732 km                                                                              ( Ans )

 

  • 4
What are you looking for?