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The distance between two vertical poles is $60 m$ . The height of one of the poles is double the height of the other. The angles of elevation of the tops of the poles from the middle point of the line segment joining their feet are complementary to each other. Find the height of the poles

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20.1, 21.21

40.41, 60.61

21.21, 42.42

50.51, 100.21

answer is C.

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Detailed Solution

$A B, P Q$ are two poles, let $P Q = h$

$\Rightarrow A B = 2 P A = 2 h$

given $B Q = 60 m$

$∠ P M Q = θ, ∠ A M B = 90 - θ$

$\begin{matrix} In Δ P Q M & In Δ A B M \\ \tan θ = \frac{P Q}{M Q} & \tan (90 ° - θ) = \frac{A B}{B M} \\ \tan θ = \frac{h}{30} \to (1) & \cot θ = \frac{2 h}{30} \to (2) \end{matrix}$

$(1) \times (2)$

$\frac{2 h^{2}}{900} = 1$

$2 h^{2} = 900$

$h^{2} = 450$

$h = 21.21$

$P Q = h = 21.21$

$A B = 2 h = 42.42$

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