Question
Sat September 22, 2012 By:
 

The shadow of a tower standing on a level ground is found 35 m longer when the sun altitude is 45 then when it is 60. Find the height of tower.

Expert Reply
Sat September 22, 2012
Answer : Given :The shadow of a tower standing on a level ground is found 35 m longer when the sun altitude is 45 then when it is 60.

Let x be the  tower's height and y be the tower's shadow height , 
according to the question we can say that when angle is 60 degrees then 
=> tan 60 =x/y..........................(1) {applying tan formula on right angle triangle}
 
when the sun's altitude is 45 , then 
=> tan 45 = x / (y+35) ..................(2) {applying tan formula  in  right angled triangle}
 
dividing eq 1 and 2 , we get
=> (tan 60 ) / tan 45 = (y+35 ) / y
=>  (underrooot 3) / 1=  (y+35 )/ y     {tan 60 =underroot 3 
                                                            and tan 45 = 1 }
 
=> y (underroot 3 ) = y + 35
=> y = 35 / ( (underroot 3)-1 )
=> y = 47.81 m (approx)
 
=> Answer : the required height of the tower is 47.81 m (approx)
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