The top of a hill observed from the top and b | vedclass

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(B) Let $AB$ be the building of height $h$ and $BP$ be the hill. Let the total height of the hill be $H = h + x$,where $x$ is the height of the hill a

Vedclass · Accepted Answer

$\frac{h \cot p}{\cot p - \cot q}$

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(B) Let $AB$ be the building of height $h$ and $BP$ be the hill. Let the total height of the hill be $H = h + x$,where $x$ is the height of the hill above the building level.From the diagram,in $	riangle ADC$,$	an p = \frac{x}{y} \Rightarrow y = x \cot p$.In $	riangle ABP$,$	an q = \frac{h + x}{y} \Rightarrow y = (h + x) \cot q$.Equating the values of $y$,we get $x \cot p = (h + x) \cot q$.$x \cot p = h \cot q + x \cot q$.$x(\cot p - \cot q) = h \cot q \Rightarrow x = \frac{h \cot q}{\cot p - \cot q}$.The total height of the hill is $H = h + x = h + \frac{h \cot q}{\cot p - \cot q} = \frac{h \cot p - h \cot q + h \cot q}{\cot p - \cot q} = \frac{h \cot p}{\cot p - \cot q}$.

The top of a hill observed from the top and bottom of a building of height $h$ is at the angle of elevation $p$ and $q$ respectively. The height of the hill is

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