question_answer

The angle of depression of vertex of a regular hexagon lying in a horizontal plane, from the top of lower of height 75 m located at the centre of the regular hexagon is 60. What is the length of each side of the hexagon?

A)  \[50\sqrt{3}\,\,\text{m}\]

B)  \[75\,\,\text{m}\]

C)  \[25\sqrt{3}\,\,\text{m}\]

D)  25 m

Correct Answer: C

Solution :

Let OG be a height of the tower

Angle of elevation = Angle of depression

In \[\Delta FOG,\]

\[\tan 60{}^\circ =\frac{75}{x}\]

\[\Rightarrow \]   \[x=\frac{75}{\sqrt{3}=25}\sqrt{3}\,\,\text{m}\]

But OF = OE = OA = OD

= OC = OB = OA

= side of hexagon

\[\therefore \] Length of hexagon \[=25\sqrt{3}\,\,\text{m}\]