A tower, of x metres high, has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant y metres from the foot of the tower. Then, the length of the flagstaff (in metres), is

Step-by-step solution

Let B C be the height of tower and C D be height of the flagstaff, Let C D=h Since, the tower and flagstaff makes equal angle, i.e. In B A C , In D A B , aligned 2 & = x+h y 2 1- ^2 & = x+h y 2 ( x y ) 1- x^2 y^2 & = x+h y 2 x y^2 & = (y^2-x^2 )(x+h) & [from Eq. (i)] x^2+x^3 & = (y^2-x^2 ) h h & = x (x^2+y^2 ) (y^2-x^2 ) aligned