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∘