Question

The angle of elevation of the Sun, if the length of the shadow of a tower is $\sqrt{3}$ times the height of the pole, is

• A. ${150}^{°}$
• B. ${30}^{°}$
• C. ${60}^{°}$
• D. ${45}^{°}$

Answer 1

The correct option is B

${30}^{°}$

Explanation for correct option:

Let

$$\begin{gathered} Ab=h, \\ Then,BC=x=h\sqrt{3} \end{gathered}$$

In $∆ABC$

$$\begin{gathered} \tan \theta =\frac{AB}{BC} \\ \Rightarrow =\frac{h}{h\sqrt{3}} \\ \Rightarrow \theta ={\tan }^{-1}\left(\frac{1}{\sqrt{3}}\right) \\ ={30}^{°} \end{gathered}$$

Hence, the correct option is B.