A vertical pole and a vertical tower are on the same level ground in such a way that, from the top of the pole, the angle of elevation of the top of the tower is 60° and the angle of depression of the bottom of the tower is 30°. If the height of the pole is 24 m, then find the height of the tower (in m).

Solution (By Examveda Team)

$$\eqalign{ & {\text{In }}\Delta ABD, \cr & \tan {30^ \circ } = \frac{P}{B} \cr & \frac{1}{{\sqrt 3 }} = \frac{{24}}{{BD}} \cr & BD = 24\sqrt 3 \cr & BD = AE = 24\sqrt 3 \cr & {\text{In }}\Delta AEC, \cr & \tan {60^ \circ } = \frac{P}{B} \cr & \sqrt 3 = \frac{{CE}}{{AE}} \cr & \sqrt 3 = \frac{{CE}}{{24\sqrt 3 }} \cr & CE = 24 \times 3 = 72 \cr & {\text{Height of tower }}CD = CE + ED \cr & = 72 + 24 = 96{\text{ cm}} \cr} $$