question_answer

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

A)  \[\frac{100}{\sqrt{3}}\,\,\text{m}\]        

B)  \[100\sqrt{3}\]

C)  86.50 m          

D)  None of these

Correct Answer: A

Solution :

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