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.

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)