question_answer

Directions: (1 - 5)

Two men on either side of a temple of 30 meters high observe its top at the angles of elevation \[\alpha \] and \[\beta \] respectively, (as shown in the figure above). The distance between the two men is \[40\sqrt{3}\] meters and the distance between the first person A and the temple is \[30\sqrt{3}\] meters. Based on the above information answer the following :

\[\angle CAB=\alpha =\]

A) \[{{\sin }^{-1}}\left( \frac{2}{\sqrt{3}} \right)\]

B) \[{{\sin }^{-1}}\left( \frac{1}{2} \right)\]

C) \[{{\sin }^{-1}}\left( 2 \right)\]

D) \[{{\sin }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]

Correct Answer: B

Solution :

\[A{{B}^{2}}={{\left( AD \right)}^{2}}+{{\left( BD \right)}^{2}}={{\left( 30\sqrt{3} \right)}^{2}}+{{\left( 30 \right)}^{2}}\] \[=2700+900=3600\] \[\Rightarrow \,AB=60\,\,m\]. \[\sin \alpha =\frac{BD}{AB}=\frac{30}{60}=\frac{1}{2}\Rightarrow \alpha ={{\sin }^{-1}}\left( \frac{1}{2} \right)\]