Two poles of equal height area standing opposite to each other on either side of a road which is 300 m wide.  From a point between them on ground, the angle of elevation of poles are 60° and 30°.  The height of each pole in meters will be?

75\(\sqrt {3}\)

In ΔABE → Tan 60° = \(\frac{H}{300 - x}\) ⇒ \(\sqrt {3}\) = \(\frac{H}{300 - x}\) ⇒ H = \(\sqrt {3}\)(300 - x) ... (i)

In ΔCDE → Tan 30° = \(\frac{H}{x}\) ⇒ H = \(\frac{x}{\sqrt {3}}\) ... (ii)

From equation (i) and (ii)

\(\sqrt {3}\)(300 - x) = \(\frac{x}{\sqrt {3}}\)

900 - 3x = x

4x = 900

x = 225

H = \(\frac{225}{\sqrt {3}}\) = 75\(\sqrt {3}\)