The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be . After moving a distance 2 metres from P towards the foot of the tower, the angle of elevation changes to . Then the height (in metres) of the tower is:

Step-by-step solution

Let AB be the tower of height ' h '. Given : In ABP = AB PB or = h x+2 (x+2) = h h= x +2 Now, In ABC , = AB BC = h x x= h Putting the value of x in eq. (2) to eq. (1), we get aligned &h= h + 2 1 & h= h +2 & aligned h( - )=2 h[ ( - )]=2 h= 2 ( - )