question_answer

A straight highway leads to the foot of a \[50\,\,m\] tall tower. From the top of the tower the angles of depression of two cars on the highway are \[{{30}^{o}}\] and\[{{60}^{o}}\]. What is the distance between the two cars?

A) \[\frac{100}{\sqrt{3}}m\]  

B) \[100\sqrt{3}m\]

C) \[86.50\,\,m\]    

D)         None of these

Correct Answer: A

Solution :

             Here,\[{{\theta }_{1}}={{60}^{o}},\,\,{{\theta }_{2}}={{30}^{o}},\,\,h=50\,\,m\]             \[h=\frac{x}{\cot {{\theta }_{2}}-\cot {{\theta }_{1}}}\]             \[x=h(\cot {{\theta }_{2}}-\cot {{\theta }_{1}})\]             \[=50\left( \sqrt{3}-\frac{1}{\sqrt{3}} \right)\]             \[=\frac{50(2)}{\sqrt{3}}=\frac{100}{\sqrt{3}}m\]