Correct option is: C) √3 : 1
Let the height of tree be BC and the length of the shadow of tree be AB.
Given that angle of elevation of the sun is \(60^\circ\)
\(\therefore\) \(\angle\)A = \(60^\circ\)
In right \(\triangle\)ABC,
tan A = \(\frac {BC}{AB}\)
= \(\frac {BC}{AB}\) = tan \(60^\circ\) = \(\sqrt3\) = \(\frac {\sqrt3}{1}\) (\(\because\) \(\angle\)A = \(60^\circ\) and tan \(60^\circ\) = \(\sqrt3\) )
\(\therefore\) BC : AB = \(\sqrt3\) : 1
Hence, the ration of height of tree with its shadow is \(\sqrt3\) : 1.
