QJEEM21Maa8dd: JEE Main 2021 Mathematics - Class 12 JEEM21Maa8dd Solution: Two poles, AB of length a metres and CD of length a + b (b ≠ a) …

Question

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Two poles, AB of length a metres and CD of length a + b (b

\neq

a) metres are erected at the same horizontal level with bases at B and D. If BD = x and tan

∠

ACB =

\frac{1}{2}

, then :

Accepted Answer

\tan θ = \frac{1}{2}

\tan (θ + α) = \frac{x}{b}, \tan α = \frac{x}{a + b}

\Rightarrow \frac{\frac{1}{2} + \frac{x}{a + b}}{1 - \frac{1}{2} \times \frac{x}{a + b}} = \frac{x}{b}

\Rightarrow x^{2} - 2 a x + a b + b^{2} = 0

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