Flag-staff of length d stands on a tower of height h if at a point on the ground the angles of elevation of the tower and the top of the flag staff be $α, β$ respectively then h

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$\frac{dcot β}{\cot α - \cot β}$

$\frac{dtan β}{\tan α - \tan β}$

$d [\frac{\tan α - \tan β}{\cot α - \cot β}]$

$d \frac{\tan α}{\tan β}$

answer is A.

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Detailed Solution

$\begin{array}{l} f r o m Δ l e APB \\ \tan α = \frac{h}{x} \Rightarrow x = hcot α \to (1) \\ ΔAPC \\ \tan β = \frac{h + d}{x} \\ x = (d + h) \cot β \to (2) \\ f r o m (1) a n d (2) \\ hcot α = (d + h) \cot β \\ hcot α = hcot β + dcot β \\ h [\cot α - \cot β] = dcot β \\ h = \frac{dcot β}{\cot α - \cot β} \end{array}$