# 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

A. $30 \sqrt{3} m$ B. $15 m$ C. $\frac{30}{\sqrt{3}} m$ D. $15 \sqrt{2} m$ Answer: Option A
Let AB be tower and a point C distance of 30 m from its foot of the tower which form an angle of elevation pf the sun of 60° $\begin{array}{l}\text{Let height of tower AB}=\text{h}\\ \text{Then in right }\triangle\text{ACB,}\\ \tan\theta=\frac{\text{ Perpendicular }}{\text{ Base }}=\frac{AB}{CB}\\ \Rightarrow\tan60^{\circ}=\frac{h}{30}\\ \Rightarrow\sqrt{3}=\frac{h}{30}\\ \Rightarrow h=30\sqrt{3}\\ \therefore\text{height of the tower}\\ =30\sqrt{3}\text{m}\end{array}$