A) \[20\,\,m\]
B) \[40\sqrt{2}\,\,m\]
C) \[40\,\,m\]
D) \[20\sqrt{2}\,\,m\]
Correct Answer: D
Solution :
From the figure, Let the diagonal of football field be = l m and height of the pole = x m \[\therefore \]In \[\Delta \,\,ABC,\tan 60{}^\circ =\frac{x}{l}\sqrt{3}=\frac{x}{l}\] \[\Rightarrow \] \[x=\sqrt{3}l\] ?(i) Now. in \[\Delta ABD,\,\,\,\tan 30{}^\circ =\frac{x}{l+80}\] \[l+80=\sqrt{3}x\] Now, from Eq. (i), \[l+80=\sqrt{3}(\sqrt{3}l)\] \[\Rightarrow \] \[l+80=3l\] \[\therefore \]\[l=\frac{80}{2}=40\,\,cm=\]diagonal of square field Hence, side of the square field is given by \[=\frac{\text{Diagonal}}{\sqrt{2}}=\frac{40}{\sqrt{2}}=20\sqrt{2}\,\,m\]You need to login to perform this action.
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