Question

The ratio of the length of a rod and its shadow is $1:\sqrt{3}$. The angle of elevation of the sun is,
A. $30{}^\circ $
B. $45{}^\circ $
C. $60{}^\circ $
D. $90{}^\circ $

Answer 1

Hint: We will be using the concept of height and distance to solve the problem. We will first draw a diagram as per the question and then apply trigonometric ratio $\tan \theta $to find the answer.

Complete step-by-step answer:

Now, we have been given that the ratio of the length of a rod and its shadow is $1:\sqrt{3}$. We have to find the angle of elevation of the sun.

Now, we will first draw a diagram as per the situation given to us.

Now, here $\theta $ is the angle of elevation of the sun.

Now, we have been given that the ratio of length of rod to its shadow i.e. $OA:OB=1:\sqrt{3}............\left( 1 \right)$

Now, we will apply the trigonometric ratio $\tan \theta \ in\ \Delta BAO$.

We know that,

$\tan \theta =\dfrac{Perpendicular}{Base}$

Now, we have AO as perpendicular and BO as base. So, we have,

$\tan \theta =\dfrac{OA}{OB}$

Now, we substitute $\dfrac{OA}{OB}$ from (1). So, we have,

$\begin{align}

  & \tan \theta =\dfrac{1}{\sqrt{3}} \\

 & \tan \theta =\tan \left( 30{}^\circ \right)\ \ \ \ \left( \because \tan \left( 30{}^\circ \right)=\dfrac{1}{\sqrt{3}} \right) \\

\end{align}$

So, we have $\theta =30{}^\circ $

Now, the angle of elevation of the sun is $30{}^\circ $.

Hence, the correct option is (A).


Note: To solve these types of questions it is important to note that we have first drawn a figure as per the question and then applied trigonometric ratio as per the figure to simplify the solution.