The angle of elevation of the top of a tower at a point on the ground level is 30 degree .After walking a distance of 100mts towards the foot of the tower along the horizontal line through the foot of the tower is 60degree.Find the height of the tower?

Answer : Let AB be the ht of the tower as h m , and BD be the original distance making and elevation of 30 degrees with angle ADB abd distance from the foot of tower = 100+x m  

and similarily , next elevation from distance x m making 60 degrees by angle ACB.

 

In triangle ABD, 

=> AB/BD= tan 30

=> h/(x+100) = 3^-1/2 ..................(1)

 

In triangle ABC, 

=> AB/BC= tan 60

=> h/x = 3^1/2 ..................(2)

dividing eq 1 and 2 , we get

 

=> x/ (x+100) = 1/3 

=> 3x = x+ 100 {cross multiplication}

=> 2x = 100 

=> x = 50 m 

 

using the value of x in eq 2 we  get 

=> h/50 = 3^1/2

=> h= 50*3^1/2 = 86.60 m (approx) is the required height of the tower Answer