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), \[\frac{h}{x}=\frac{h+6}{x+2\sqrt{3}}\] \[\Rightarrow \] \[h(x+2\sqrt{3})=x(h+6)\] \[\Rightarrow \] \[2\sqrt{3}h=6x\] \[\Rightarrow \] \[x=\frac{h}{\sqrt{3}}\] \[\therefore \] \[\tan \phi =\frac{h}{x}\Rightarrow \tan \phi =\sqrt{3}\] \[\Rightarrow \] \[\phi ={{60}^{o}}\]You need to login to perform this action.
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