Two poles stand on a horizontal plane, P and Q are two points on the line joining the base of the poles and between them. The angle of elevation of the top of the poles as seen from P are 30 and 60 and as seen from Q are 60 and 45. If the length of PQ is 30m. Find the heights of the poles and the distance between them.   

Dear Student,

Please find below the solution to the asked query:

We form our diagram from given information , As :

Here height of mole =  AB and CD   and PQ  = 30 m (  Given )

We know : θ = OppositeAdjacent , So

In AQB we get

tan 60° = ABAQ3= ABAQ        (  we know tan 60° = 3 )AB =AQ 3            --- ( 1 )
And
In APB we get

tan 30° = ABAP13 = ABAQ + PQ        (  we know tan 30° =13 )13 = AQ 3AQ + 30        ( From equation 1 )AQ + 30= 3 AQ 2 AQ =30 AQ =15                     --- ( 2 )
Substitute value from equation 2 in equation 1 we get

AB  =  15 3 =  15 × 1.732 = 25.98
 And In APC we get

tan 60° = CDCP3= CDCP        (  we know tan 60° = 3 )CD =CP 3            --- ( 3 )
And
In AQC we get

tan 45° = CDCQ1 = CDCP + PQ        (  we know tan 45° =1 )1 = CP 3CP + 30        ( From equation 3 )CP + 30= 3 CP CP 3 - 1 =30 CP =30 3 - 1 CP =30 3 - 1 × 3 + 1  3 + 1 CP =30 3 +13 + 3 - 3 - 1CP =30 3 +12CP =15 3 +1CP =15 1.732 +1         (  We know 3  1.732 )CP =15 × 2.732CP =40.98
Substitute that value in equation 3 we get

CD  =  40.983 =  40.98× 1.732 = 70.97736 70.98

Therefore,

Height of poles :  AB  = 25.98 m and CD  = 70.98 m

And

Distance between given poles =  AQ +  PQ +  CP =  15 + 30  + 40.98 = 85.98 m                                      ( Ans )



Hope this information will clear your doubts about topic.

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards

  • 6
diagam plz 
  • -4
What are you looking for?