• # question_answer 7) From the top of a tower, 100 m high, a man observes two cars on the opposite sides of the tower and in same straight line with its base, with angles of depression $30{}^\circ$ and $45{}^\circ$. Find the distance between the cars. [Take $\sqrt{3}=1.732$]

 Let AB is a tower. Cars are at point C and D respectively In $\Delta \,ABC$, $\frac{AB}{BC}=\tan \,\,30{}^\circ$ $\frac{100}{x}=\frac{1}{\sqrt{3}}$ $x=100\sqrt{3}$ $=100\times 1.732$ $=173.2\,\,m$ In $\Delta \,ABD$, $\frac{AB}{BD}=\tan \,\,45{}^\circ$ $\frac{100}{y}=1$ $y=100\,m$ Distance between two cars $=x+y$ $=173.2+100$ $=273.2\,m$