question_answer

If a flag-staff of 6 m high placed on the top of a tower throws a shadow of \[2\sqrt{3}m\] along the ground, then the angle that the Sun makes with the ground is

A)  \[{{60}^{o}}\]                    

B)  \[{{30}^{o}}\]

C)  \[{{90}^{o}}\]                    

D)  None of these

Correct Answer: A

Solution :

Let OA and AB be the shadows of tower OR and flag-staff TO respectively on the grounds. Let the Sun makes an angle ^ with the ground. Let \[OA=x\] In right angled \[\Delta AOR,\] \[\tan \phi =\frac{h}{x}\]                       ...(i) and in \[\Delta BOQ.\] \[\tan \phi =\frac{h+6}{x+2\sqrt{3}}\]             ...(ii) From Eqs. (i) and (ii), \[\frac{h}{x}=\frac{h+6}{x+2\sqrt{3}}\] \[\Rightarrow \]            \[h(x+2\sqrt{3})=x(h+6)\] \[\Rightarrow \]            \[2\sqrt{3}h=6x\] \[\Rightarrow \]            \[x=\frac{h}{\sqrt{3}}\] \[\therefore \]    \[\tan \phi =\frac{h}{x}\Rightarrow \tan \phi =\sqrt{3}\] \[\Rightarrow \]            \[\phi ={{60}^{o}}\]