Two poles of equal height are standing opposite to each other, on either side of a road, which is 100 m wide. From a…

CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 5 Marks · July 2025 · Standard

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605 Marks · July 2025 · Standard

Two poles of equal height are standing opposite to each other, on either side of a road, which is $100$ m wide. From a point between them on the road, the angles of elevation of the top of the poles are $60^{\circ}$ and $30^{\circ}$ respectively. Find the height of the poles.

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Let 'h' be the height of pole.
$\frac{h}{x} = \tan 60^{\circ} = \sqrt{3}$
$\Rightarrow h = \sqrt{3}x$ --- (1)
Also, $\frac{h}{100-x} = \tan 30^{\circ} = \frac{1}{\sqrt{3}}$
$\Rightarrow h = \frac{100 - x}{\sqrt{3}}$ --- (2)
From (1) and (2), we get $x = 25$
Hence, $h = 25\sqrt{3}$ m