Question

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

(a) 50√3 m

(b) 75 m

(c) 25√3 m

(d) 25 m

Answer 1

Correct option is (c) 25√3 m

Let OP be the tower of height 75 m.

Angle of elevation = Angle of depression

\(\therefore\) In \(\triangle\)FOP,

\(\tan 60° = \frac{75}x\)

⇒ \(x = \frac{75}{\sqrt 3} = 25\sqrt 3 \, m\)

In a regular hexagon, six equilateral \(\triangle\)s are formed, i.e.,

OF = OE = OD = OC = OB = OA = side of hexagon

⇒ length of hexagon = 25√3 m.