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 AShow Answer
Solution(By Apex Team)
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°
$\begin{array}{l}\text{Let height of tower AB}=\text{h}\\
\text{Then in right }\triangle\text{ACB,}\\
\tan\theta=\frac{\text{ Perpendicular }}{\text{ Base }}=\frac{AB}{CB}\\
\Rightarrow\tan60^{\circ}=\frac{h}{30}\\
\Rightarrow\sqrt{3}=\frac{h}{30}\\
\Rightarrow h=30\sqrt{3}\\
\therefore\text{height of the tower}\\
=30\sqrt{3}\text{m}\end{array}$
$\begin{array}{l}\text{Let height of tower AB}=\text{h}\\
\text{Then in right }\triangle\text{ACB,}\\
\tan\theta=\frac{\text{ Perpendicular }}{\text{ Base }}=\frac{AB}{CB}\\
\Rightarrow\tan60^{\circ}=\frac{h}{30}\\
\Rightarrow\sqrt{3}=\frac{h}{30}\\
\Rightarrow h=30\sqrt{3}\\
\therefore\text{height of the tower}\\
=30\sqrt{3}\text{m}\end{array}$
