question_answer

If a pole of height \[51\sqrt{3}\] meter cast a shadow of length 153 meter long on the ground, then on that time find the angle of elevation of the Sun.

A)  \[45{}^\circ \]                         

B)  \[30{}^\circ \]

C)  \[60{}^\circ \]                         

D)  \[90{}^\circ \]

Correct Answer: B

Solution :

Let AB is the height of pole and BC is the length of shadow of the pole. Then, In \[\Delta ABC,\] \[\tan \theta =\frac{AB}{BC}=\frac{51\sqrt{3}}{153}\] \[\tan \theta =\frac{\sqrt{3}}{3}=\frac{1}{\sqrt{3}}=\tan 30{}^\circ \,\,\therefore \,\,\,\theta =\underline{\mathbf{30{}^\circ }}\]