Question

At a certain instant the ratio of the lengths of a pillar and its shadow are in the ratio $1:\sqrt{3}$. At that instant, the angle of elevation of the sum is

(a) 30°
(b) 45°
(c) 60°
(d) none of these

Answer 1

(a) 30°
Let $AB$ be the pillar and $AC$ be its shadow.
Let:
∠$ACB=\theta$ and $AB:BC=1:\sqrt{3}$

In the right ∆$ABC$, we have:
$\frac{AB}{AC}=\tan \theta$

$$\begin{gathered} \Rightarrow \frac{k}{\sqrt{3}k}=\tan \theta \\ \Rightarrow \frac{1}{\sqrt{3}}=\tan \theta \\ \Rightarrow \tan 30°=\tan \theta \end{gathered}$$
⇒ $\theta ={30}^o$ [∵ $\tan {30}^o=\frac{1}{\sqrt{3}}$]
Hence, the angle of elevation of the sun is ${30}^o$.