The length of shadow of a tower on the plane ground is $\sqrt{3}$ times the height of the tower. The angle of elevation of sun is.
A. 45° B. 30° C. 60° D. 90° Answer: Option BShow Answer
Solution(By Apex Team)
Let AB be tower and BC be its shadow
∴ Let AB = x
$\begin{array}{l}\text{Then BC}=\sqrt{3}\times x\\
=\sqrt{3}x\\
\begin{aligned}\therefore\tan\theta&=\frac{AB}{BC}\\
&=\frac{x}{\sqrt{3}x}\\
&=\frac{1}{\sqrt{3}}\\
&=\tan30^{\circ}\\
\therefore\theta=30^{\circ}&\\
&\end{aligned}\end{array}$
∴ Angle of elevation of the sun = 30∘
$\begin{array}{l}\text{Then BC}=\sqrt{3}\times x\\
=\sqrt{3}x\\
\begin{aligned}\therefore\tan\theta&=\frac{AB}{BC}\\
&=\frac{x}{\sqrt{3}x}\\
&=\frac{1}{\sqrt{3}}\\
&=\tan30^{\circ}\\
\therefore\theta=30^{\circ}&\\
&\end{aligned}\end{array}$
∴ Angle of elevation of the sun = 30∘
