Let A and B be two towers with the same base. From the mid point of the line joining their feet, the angles of elevation of the tops of A and B are 30° and 45° respectively. The ratio of the heights of A and B is:

Solution (By Examveda Team)

$$\eqalign{ & \tan {30^ \circ } = \frac{{{h_A}}}{x} \cr & {h_A} = \frac{1}{{\sqrt 3 }}x{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {\text{i}} \right) \cr & {h_B} = x{\text{ }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {{\text{ii}}} \right) \cr & \frac{{{h_A}}}{{{h_B}}} = \frac{1}{{\sqrt 3 }} \cr} $$