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

Answer: Option A

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°

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