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?
Answer & explanation
Correct answer: option 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\(\sqrt {3}\)