question_answer

The shadow of a pole is\[\sqrt{3}\]times longer. The angle of elevation is equal to:

A)  \[40{}^\circ \]                                  

B)  \[\frac{45{}^\circ }{2}\]

C)  \[60{}^\circ \]                  

D)         \[30{}^\circ \]

E)  \[90{}^\circ \]

Correct Answer: D

Solution :

Let BC = h, then \[AB=\sqrt{3}h\] In \[\Delta ABC\] \[\tan \theta =\frac{BC}{AB}=\frac{h}{\sqrt{3}h}\] \[\Rightarrow \]               \[\tan \theta =\frac{1}{\sqrt{3}}=\tan 30{}^\circ \] \[\Rightarrow \]               \[\theta =30{}^\circ \]