If the altitude of the sun is at 60°, then the height of the vertical tower that will cast a shadow of length 30 m is

Solution (By Examveda Team)

Let AB be tower and a point P distance of 30 m from its foot of the tower which form an angle of elevation pf the sun of 60°

$$\eqalign{ & {\text{Let height of tower }}AB = h \cr & {\text{Then in right }}\Delta APB, \cr & \tan \theta = \frac{{{\text{Perpendicular}}}}{{{\text{Base}}}} = \frac{{AB}}{{PB}} \cr & \Rightarrow \tan {60^ \circ } = \frac{h}{{30}} \cr & \Rightarrow \sqrt 3 = \frac{h}{{30}} \cr & \Rightarrow h = 30\sqrt 3 \cr} $$
∴ Height of the tower $$ = 30\sqrt 3 \,m$$